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-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# Data Types, Graphical Marks, and Visual Encoding Channels\n",
- "\n",
- "A visualization represents data using a collection of *graphical marks*\n",
- "(bars, lines, points, etc.). The attributes of a mark — such as its\n",
- "position, shape, size, or color — serve as *channels* through which we\n",
- "can encode underlying data values.\n",
- "\n",
- "With a basic framework of *data types*, *marks*, and *encoding\n",
- "channels*, we can concisely create a wide variety of visualizations. In\n",
- "this notebook, we explore each of these elements and show how to use\n",
- "them to create custom statistical graphics.\n",
- "\n",
- "*This notebook is part of the [data visualization\n",
- "curriculum](https://github.com/uwdata/visualization-curriculum).*"
- ],
- "id": "e963f1b6-4697-4855-86db-dfb698d8ec13"
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {},
- "outputs": [],
- "source": [
- "import pandas as pd\n",
- "import altair as alt"
- ],
- "id": "2720a589-c3e0-43c9-ac72-70ad51a461c4"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Global Development Data\n",
- "\n",
- "We will be visualizing global health and population data for a number of\n",
- "countries, over the time period of 1955 to 2005. The data was collected\n",
- "by the [Gapminder Foundation](https://www.gapminder.org/) and shared in\n",
- "[Hans Rosling’s popular TED\n",
- "talk](https://www.youtube.com/watch?v=hVimVzgtD6w). If you haven’t seen\n",
- "the talk, we encourage you to watch it first!\n",
- "\n",
- "Let’s first load the dataset from the\n",
- "[vega-datasets](https://github.com/vega/vega-datasets) collection into a\n",
- "Pandas data frame."
- ],
- "id": "eeb59a95-9b35-4c7b-a368-22190fe3798d"
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {},
- "outputs": [],
- "source": [
- "from vega_datasets import data as vega_data\n",
- "data = vega_data.gapminder()"
- ],
- "id": "2f466eb3-7183-4eec-b2ba-5f07e0a97e31"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "How big is the data?"
- ],
- "id": "f78977b6-ac44-4e4d-9071-92fa2767d8d7"
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {
- "outputId": "134a2f4a-c15d-4fcd-fd93-49b26a4f5e30"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/plain": [
- "(693, 6)"
- ]
- }
- }
- ],
- "source": [
- "data.shape"
- ],
- "id": "fd87f460-366b-4c23-bd7d-bda99b849f73"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "693 rows and 6 columns! Let’s take a peek at the data content:"
- ],
- "id": "b0e7b812-6323-43d8-8ddf-8eee5317eda2"
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {
- "outputId": "ec103505-4d8f-4310-a6e1-7eea3d789c28"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "data.head(5)"
- ],
- "id": "2c66aa69-0f67-4309-be86-ba210645688e"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "For each `country` and `year` (in 5-year intervals), we have measures of\n",
- "fertility in terms of the number of children per woman (`fertility`),\n",
- "life expectancy in years (`life_expect`), and total population (`pop`).\n",
- "\n",
- "We also see a `cluster` field with an integer code. What might this\n",
- "represent? We’ll try and solve this mystery as we visualize the data!\n",
- "\n",
- "Let’s also create a smaller data frame, filtered down to values for the\n",
- "year 2000 only:"
- ],
- "id": "a9d43206-56d0-405b-8381-03e3ba789857"
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {},
- "outputs": [],
- "source": [
- "data2000 = data.loc[data['year'] == 2000]"
- ],
- "id": "fa793dfa-ccdb-43f3-b80d-e1ad5d78a3b6"
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {
- "outputId": "8629f998-e723-4b92-9a95-f0df3c9843a8"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "data2000.head(5)"
- ],
- "id": "d8b2057d-889c-4bdb-bd23-3d8f1fadae9e"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Data Types\n",
- "\n",
- "The first ingredient in effective visualization is the input data. Data\n",
- "values can represent different forms of measurement. What kinds of\n",
- "comparisons do those measurements support? And what kinds of visual\n",
- "encodings then support those comparisons?\n",
- "\n",
- "We will start by looking at the basic data types that Altair uses to\n",
- "inform visual encoding choices. These data types determine the kinds of\n",
- "comparisons we can make, and thereby guide our visualization design\n",
- "decisions.\n",
- "\n",
- "### Nominal (N)\n",
- "\n",
- "*Nominal* data (also called *categorical* data) consist of category\n",
- "names.\n",
- "\n",
- "With nominal data we can compare the equality of values: *is value A the\n",
- "same or different than value B? (A = B)*, supporting statements like “A\n",
- "is equal to B” or “A is not equal to B”. In the dataset above, the\n",
- "`country` field is nominal.\n",
- "\n",
- "When visualizing nominal data we should readily be able to see if values\n",
- "are the same or different: position, color hue (blue, red, green,\n",
- "*etc.*), and shape can help. However, using a size channel to encode\n",
- "nominal data might mislead us, suggesting rank-order or magnitude\n",
- "differences among values that do not exist!\n",
- "\n",
- "### Ordinal (O)\n",
- "\n",
- "*Ordinal* data consist of values that have a specific ordering.\n",
- "\n",
- "With ordinal data we can compare the rank-ordering of values: *does\n",
- "value A come before or after value B? (A \\< B)*, supporting statements\n",
- "like “A is less than B” or “A is greater than B”. In the dataset above,\n",
- "we can treat the `year` field as ordinal.\n",
- "\n",
- "When visualizing ordinal data, we should perceive a sense of rank-order.\n",
- "Position, size, or color value (brightness) might be appropriate, where\n",
- "as color hue (which is not perceptually ordered) would be less\n",
- "appropriate.\n",
- "\n",
- "### Quantitative (Q)\n",
- "\n",
- "With *quantitative* data we can measure numerical differences among\n",
- "values. There are multiple sub-types of quantitative data:\n",
- "\n",
- "For *interval* data we can measure the distance (interval) between\n",
- "points: *what is the distance to value A from value B? (A - B)*,\n",
- "supporting statements such as “A is 12 units away from B”.\n",
- "\n",
- "For *ratio* data the zero-point is meaningful and so we can also measure\n",
- "proportions or scale factors: *value A is what proportion of value B? (A\n",
- "/ B)*, supporting statements such as “A is 10% of B” or “B is 7 times\n",
- "larger than A”.\n",
- "\n",
- "In the dataset above, `year` is a quantitative interval field (the value\n",
- "of year “zero” is subjective), whereas `fertility` and `life_expect` are\n",
- "quantitative ratio fields (zero is meaningful for calculating\n",
- "proportions). Vega-Lite represents quantitative data, but does not make\n",
- "a distinction between interval and ratio types.\n",
- "\n",
- "Quantitative values can be visualized using position, size, or color\n",
- "value, among other channels. An axis with a zero baseline is essential\n",
- "for proportional comparisons of ratio values, but can be safely omitted\n",
- "for interval comparisons.\n",
- "\n",
- "### Temporal (T)\n",
- "\n",
- "*Temporal* values measure time points or intervals. This type is a\n",
- "special case of quantitative values (timestamps) with rich semantics and\n",
- "conventions (i.e., the [Gregorian\n",
- "calendar](https://en.wikipedia.org/wiki/Gregorian_calendar)). The\n",
- "temporal type in Vega-Lite supports reasoning about time units (year,\n",
- "month, day, hour, etc.), and provides methods for requesting specific\n",
- "time intervals.\n",
- "\n",
- "Example temporal values include date strings such as `“2019-01-04”` and\n",
- "`“Jan 04 2019”`, as well as standardized date-times such as the [ISO\n",
- "date-time format](https://en.wikipedia.org/wiki/ISO_8601):\n",
- "`“2019-01-04T17:50:35.643Z”`.\n",
- "\n",
- "There are no temporal values in our global development dataset above, as\n",
- "the `year` field is simply encoded as an integer. For more details about\n",
- "using temporal data in Altair, see the [Times and Dates\n",
- "documentation](https://altair-viz.github.io/user_guide/times_and_dates.html).\n",
- "\n",
- "### Summary\n",
- "\n",
- "These data types are not mutually exclusive, but rather form a\n",
- "hierarchy: ordinal data support nominal (equality) comparisons, while\n",
- "quantitative data support ordinal (rank-order) comparisons.\n",
- "\n",
- "Moreover, these data types do *not* provide a fixed categorization. Just\n",
- "because a data field is represented using a number doesn’t mean we have\n",
- "to treat it as a quantitative type! For example, we might interpret a\n",
- "set of ages (10 years old, 20 years old, etc) as nominal (underage or\n",
- "overage), ordinal (grouped by year), or quantitative (calculate average\n",
- "age).\n",
- "\n",
- "Now let’s examine how to visually encode these data types!\n",
- "\n",
- "## Encoding Channels\n",
- "\n",
- "At the heart of Altair is the use of *encodings* that bind data fields\n",
- "(with a given data type) to available encoding *channels* of a chosen\n",
- "*mark* type. In this notebook we’ll examine the following encoding\n",
- "channels:\n",
- "\n",
- "- `x`: Horizontal (x-axis) position of the mark.\n",
- "- `y`: Vertical (y-axis) position of the mark.\n",
- "- `size`: Size of the mark. May correspond to area or length,\n",
- " depending on the mark type.\n",
- "- `color`: Mark color, specified as a [legal CSS\n",
- " color](https://developer.mozilla.org/en-US/docs/Web/CSS/color_value).\n",
- "- `opacity`: Mark opacity, ranging from 0 (fully transparent) to 1\n",
- " (fully opaque).\n",
- "- `shape`: Plotting symbol shape for `point` marks.\n",
- "- `tooltip`: Tooltip text to display upon mouse hover over the mark.\n",
- "- `order`: Mark ordering, determines line/area point order and drawing\n",
- " order.\n",
- "- `column`: Facet the data into horizontally-aligned subplots.\n",
- "- `row`: Facet the data into vertically-aligned subplots.\n",
- "\n",
- "For a complete list of available channels, see the [Altair encoding\n",
- "documentation](https://altair-viz.github.io/altair-viz-v4/user_guide/encoding.html).\n",
- "\n",
- "### X\n",
- "\n",
- "The `x` encoding channel sets a mark’s horizontal position\n",
- "(x-coordinate). In addition, default choices of axis and title are made\n",
- "automatically. In the chart below, the choice of a quantitative data\n",
- "type results in a continuous linear axis scale:"
- ],
- "id": "6866dbca-e4fc-42e3-bf8e-eeb0b0ea574b"
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {
- "outputId": "2a958755-7f70-4a86-ab6f-2cfb24ad7231"
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- "outputs": [
- {
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- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_point().encode(\n",
- " alt.X('fertility:Q')\n",
- ")"
- ],
- "id": "3d277984-d18b-44fe-8f77-c48e799af283"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Y\n",
- "\n",
- "The `y` encoding channel sets a mark’s vertical position (y-coordinate).\n",
- "Here we’ve added the `cluster` field using an ordinal (`O`) data type.\n",
- "The result is a discrete axis that includes a sized band, with a default\n",
- "step size, for each unique value:"
- ],
- "id": "2339d5ba-7f49-453a-a585-62d6a05fb8e1"
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {
- "outputId": "9ff5b4a8-143c-4595-845f-026ed2e747a8"
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- "outputs": [
- {
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- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_point().encode(\n",
- " alt.X('fertility:Q'),\n",
- " alt.Y('cluster:O')\n",
- ")"
- ],
- "id": "8fe17170-314e-4f8c-991c-aecf823f0533"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "*What happens to the chart above if you swap the `O` and `Q` field\n",
- "types?*\n",
- "\n",
- "If we instead add the `life_expect` field as a quantitative (`Q`)\n",
- "variable, the result is a scatter plot with linear scales for both axes:"
- ],
- "id": "f27f9ca2-c0a6-4cd3-89d5-f9b76b1a4755"
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {
- "outputId": "ac41eaeb-4872-48db-ddf1-ab6b5c84f387"
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- "outputs": [
- {
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- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_point().encode(\n",
- " alt.X('fertility:Q'),\n",
- " alt.Y('life_expect:Q')\n",
- ")"
- ],
- "id": "0ee72e9e-7325-468e-aa2a-4a1c0b31fc98"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "By default, axes for linear quantitative scales include zero to ensure a\n",
- "proper baseline for comparing ratio-valued data. In some cases, however,\n",
- "a zero baseline may be meaningless or you may want to focus on interval\n",
- "comparisons. To disable automatic inclusion of zero, configure the scale\n",
- "mapping using the encoding `scale` attribute:"
- ],
- "id": "80dacfdf-85dc-492a-9288-4cc90ba5302d"
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "metadata": {
- "outputId": "8cb0ca55-176b-4d2f-8891-2c124276e429"
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- {
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- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_point().encode(\n",
- " alt.X('fertility:Q', scale=alt.Scale(zero=False)),\n",
- " alt.Y('life_expect:Q', scale=alt.Scale(zero=False))\n",
- ")"
- ],
- "id": "c8f7d634-8fbd-4a33-88d7-3628deef3fb5"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Now the axis scales no longer include zero by default. Some padding\n",
- "still remains, as the axis domain end points are automatically snapped\n",
- "to *nice* numbers like multiples of 5 or 10.\n",
- "\n",
- "*What happens if you also add `nice=False` to the scale attribute\n",
- "above?*\n",
- "\n",
- "### Size\n",
- "\n",
- "The `size` encoding channel sets a mark’s size or extent. The meaning of\n",
- "the channel can vary based on the mark type. For `point` marks, the\n",
- "`size` channel maps to the pixel area of the plotting symbol, such that\n",
- "the diameter of the point matches the square root of the size value.\n",
- "\n",
- "Let’s augment our scatter plot by encoding population (`pop`) on the\n",
- "`size` channel. As a result, the chart now also includes a legend for\n",
- "interpreting the size values."
- ],
- "id": "c8d1d83c-3e90-4fab-9915-2757f22585e8"
- },
- {
- "cell_type": "code",
- "execution_count": 11,
- "metadata": {
- "outputId": "4f76557c-4e35-41fc-9e06-513be34969ae"
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- {
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- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_point().encode(\n",
- " alt.X('fertility:Q'),\n",
- " alt.Y('life_expect:Q'),\n",
- " alt.Size('pop:Q')\n",
- ")"
- ],
- "id": "b111834d-6988-4708-a57c-f3904f112b8e"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In some cases we might be unsatisfied with the default size range. To\n",
- "provide a customized span of sizes, set the `range` parameter of the\n",
- "`scale` attribute to an array indicating the smallest and largest sizes.\n",
- "Here we update the size encoding to range from 0 pixels (for zero\n",
- "values) to 1,000 pixels (for the maximum value in the scale domain):"
- ],
- "id": "5decfd95-f45a-46ab-a3f7-7caca88e3149"
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "metadata": {
- "outputId": "0d88f561-9737-43fa-a84a-7ad6dcdfbf0c"
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- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_point().encode(\n",
- " alt.X('fertility:Q'),\n",
- " alt.Y('life_expect:Q'),\n",
- " alt.Size('pop:Q', scale=alt.Scale(range=[0,1000]))\n",
- ")"
- ],
- "id": "4ce26f0f-2975-4982-9a00-49a86ee7b9ae"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Color and Opacity\n",
- "\n",
- "The `color` encoding channel sets a mark’s color. The style of color\n",
- "encoding is highly dependent on the data type: nominal data will default\n",
- "to a multi-hued qualitative color scheme, whereas ordinal and\n",
- "quantitative data will use perceptually ordered color gradients.\n",
- "\n",
- "Here, we encode the `cluster` field using the `color` channel and a\n",
- "nominal (`N`) data type, resulting in a distinct hue for each cluster\n",
- "value. Can you start to guess what the `cluster` field might indicate?"
- ],
- "id": "f6c42427-a8f5-4bc9-9f45-4e979cce2088"
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "metadata": {
- "outputId": "f12aeb57-07c5-422e-8cb1-62253b545af8"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_point().encode(\n",
- " alt.X('fertility:Q'),\n",
- " alt.Y('life_expect:Q'),\n",
- " alt.Size('pop:Q', scale=alt.Scale(range=[0,1000])),\n",
- " alt.Color('cluster:N')\n",
- ")"
- ],
- "id": "933c2e97-0b39-4920-86af-3e180d6b28d2"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "If we prefer filled shapes, we can can pass a `filled=True` parameter to\n",
- "the `mark_point` method:"
- ],
- "id": "c6dffa59-b80b-4b15-9093-c5af0abf2cd3"
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "metadata": {
- "outputId": "8aba4f13-bfe3-43b1-e3ea-554a8d20b7f5"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_point(filled=True).encode(\n",
- " alt.X('fertility:Q'),\n",
- " alt.Y('life_expect:Q'),\n",
- " alt.Size('pop:Q', scale=alt.Scale(range=[0,1000])),\n",
- " alt.Color('cluster:N')\n",
- ")"
- ],
- "id": "06e539a6-6fd7-4438-a976-d91ad4b11f1b"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "By default, Altair uses a bit of transparency to help combat\n",
- "over-plotting. We are free to further adjust the opacity, either by\n",
- "passing a default value to the `mark_*` method, or using a dedicated\n",
- "encoding channel.\n",
- "\n",
- "Here we demonstrate how to provide a constant value to an encoding\n",
- "channel instead of binding a data field:"
- ],
- "id": "7fa6c924-8908-42a0-9488-390080374298"
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "metadata": {
- "outputId": "2dd14842-8fd5-4997-ea47-91cd489e0193"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_point(filled=True).encode(\n",
- " alt.X('fertility:Q'),\n",
- " alt.Y('life_expect:Q'),\n",
- " alt.Size('pop:Q', scale=alt.Scale(range=[0,1000])),\n",
- " alt.Color('cluster:N'),\n",
- " alt.OpacityValue(0.5)\n",
- ")"
- ],
- "id": "a61246d0-09e2-46c4-b6b5-93620dbb8a99"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Shape\n",
- "\n",
- "The `shape` encoding channel sets the geometric shape used by `point`\n",
- "marks. Unlike the other channels we have seen so far, the `shape`\n",
- "channel can not be used by other mark types. The shape encoding channel\n",
- "should only be used with nominal data, as perceptual rank-order and\n",
- "magnitude comparisons are not supported.\n",
- "\n",
- "Let’s encode the `cluster` field using `shape` as well as `color`. Using\n",
- "multiple channels for the same underlying data field is known as a\n",
- "*redundant encoding*. The resulting chart combines both color and shape\n",
- "information into a single symbol legend:"
- ],
- "id": "e73b515b-f27a-4725-8d9d-2553f2850345"
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "metadata": {
- "outputId": "e418f006-988c-42a9-9a81-664d1d52d93c"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_point(filled=True).encode(\n",
- " alt.X('fertility:Q'),\n",
- " alt.Y('life_expect:Q'),\n",
- " alt.Size('pop:Q', scale=alt.Scale(range=[0,1000])),\n",
- " alt.Color('cluster:N'),\n",
- " alt.OpacityValue(0.5),\n",
- " alt.Shape('cluster:N')\n",
- ")"
- ],
- "id": "b072fe6e-8173-4726-adc7-067d7892c75d"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Tooltips & Ordering\n",
- "\n",
- "By this point, you might feel a bit frustrated: we’ve built up a chart,\n",
- "but we still don’t know what countries the visualized points correspond\n",
- "to! Let’s add interactive tooltips to enable exploration.\n",
- "\n",
- "The `tooltip` encoding channel determines tooltip text to show when a\n",
- "user moves the mouse cursor over a mark. Let’s add a tooltip encoding\n",
- "for the `country` field, then investigate which countries are being\n",
- "represented."
- ],
- "id": "1352d37d-467e-469f-b799-92f7a9678642"
- },
- {
- "cell_type": "code",
- "execution_count": 17,
- "metadata": {
- "outputId": "f13ddd14-3b6f-4f96-ca08-8d3b2ba94a34"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_point(filled=True).encode(\n",
- " alt.X('fertility:Q'),\n",
- " alt.Y('life_expect:Q'),\n",
- " alt.Size('pop:Q', scale=alt.Scale(range=[0,1000])),\n",
- " alt.Color('cluster:N'),\n",
- " alt.OpacityValue(0.5),\n",
- " alt.Tooltip('country')\n",
- ")"
- ],
- "id": "86266886-d7c0-4cae-94d6-152eba5546a7"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "As you mouse around you may notice that you can not select some of the\n",
- "points. For example, the largest dark blue circle corresponds to India,\n",
- "which is drawn on top of a country with a smaller population, preventing\n",
- "the mouse from hovering over that country. To fix this problem, we can\n",
- "use the `order` encoding channel.\n",
- "\n",
- "The `order` encoding channel determines the order of data points,\n",
- "affecting both the order in which they are drawn and, for `line` and\n",
- "`area` marks, the order in which they are connected to one another.\n",
- "\n",
- "Let’s order the values in descending rank order by the population\n",
- "(`pop`), ensuring that smaller circles are drawn later than larger\n",
- "circles:"
- ],
- "id": "011f3a86-1583-41e2-83a0-562e796b6bc0"
- },
- {
- "cell_type": "code",
- "execution_count": 18,
- "metadata": {
- "outputId": "3b7254de-09f3-4850-f066-ea8318ec5479"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_point(filled=True).encode(\n",
- " alt.X('fertility:Q'),\n",
- " alt.Y('life_expect:Q'),\n",
- " alt.Size('pop:Q', scale=alt.Scale(range=[0,1000])),\n",
- " alt.Color('cluster:N'),\n",
- " alt.OpacityValue(0.5),\n",
- " alt.Tooltip('country:N'),\n",
- " alt.Order('pop:Q', sort='descending')\n",
- ")"
- ],
- "id": "94edd2bd-7313-489c-9be4-b942e72052b7"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Now we can identify the smaller country being obscured by India: it’s\n",
- "Bangladesh!\n",
- "\n",
- "We can also now figure out what the `cluster` field represents. Mouse\n",
- "over the various colored points to formulate your own explanation.\n",
- "\n",
- "At this point we’ve added tooltips that show only a single property of\n",
- "the underlying data record. To show multiple values, we can provide the\n",
- "`tooltip` channel an array of encodings, one for each field we want to\n",
- "include:"
- ],
- "id": "46461ab1-ce28-4643-8280-1b74653e4721"
- },
- {
- "cell_type": "code",
- "execution_count": 19,
- "metadata": {
- "outputId": "ee47eb3b-146d-4c6b-dfa7-94ddeb0fc5d3"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_point(filled=True).encode(\n",
- " alt.X('fertility:Q'),\n",
- " alt.Y('life_expect:Q'),\n",
- " alt.Size('pop:Q', scale=alt.Scale(range=[0,1000])),\n",
- " alt.Color('cluster:N'),\n",
- " alt.OpacityValue(0.5),\n",
- " alt.Order('pop:Q', sort='descending'),\n",
- " tooltip = [\n",
- " alt.Tooltip('country:N'),\n",
- " alt.Tooltip('fertility:Q'),\n",
- " alt.Tooltip('life_expect:Q')\n",
- " ] \n",
- ")"
- ],
- "id": "faac490c-d220-4e21-95ea-40a87a026de0"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Now we can see multiple data fields upon mouse over!\n",
- "\n",
- "### Column and Row Facets\n",
- "\n",
- "Spatial position is one of the most powerful and flexible channels for\n",
- "visual encoding, but what can we do if we already have assigned fields\n",
- "to the `x` and `y` channels? One valuable technique is to create a\n",
- "*trellis plot*, consisting of sub-plots that show a subset of the data.\n",
- "A trellis plot is one example of the more general technique of\n",
- "presenting data using [small\n",
- "multiples](https://en.wikipedia.org/wiki/Small_multiple) of views.\n",
- "\n",
- "The `column` and `row` encoding channels generate either a horizontal\n",
- "(columns) or vertical (rows) set of sub-plots, in which the data is\n",
- "partitioned according to the provided data field.\n",
- "\n",
- "Here is a trellis plot that divides the data into one column per\n",
- "\\`cluster\\` value:"
- ],
- "id": "46e12687-413c-4702-9db6-48f7ce19dd5e"
- },
- {
- "cell_type": "code",
- "execution_count": 20,
- "metadata": {
- "outputId": "b62aff8e-a2aa-409a-be1d-4cf3708f9ab3"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_point(filled=True).encode(\n",
- " alt.X('fertility:Q'),\n",
- " alt.Y('life_expect:Q'),\n",
- " alt.Size('pop:Q', scale=alt.Scale(range=[0,1000])),\n",
- " alt.Color('cluster:N'),\n",
- " alt.OpacityValue(0.5),\n",
- " alt.Tooltip('country:N'),\n",
- " alt.Order('pop:Q', sort='descending'),\n",
- " alt.Column('cluster:N')\n",
- ")"
- ],
- "id": "ab597f3a-0799-45cf-97bb-0078dd34812a"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The plot above does not fit on screen, making it difficult to compare\n",
- "all the sub-plots to each other! We can set the default `width` and\n",
- "`height` properties to create a smaller set of multiples. Also, as the\n",
- "column headers already label the `cluster` values, let’s remove our\n",
- "`color` legend by setting it to `None`. To make better use of space we\n",
- "can also orient our `size` legend to the `'bottom'` of the chart."
- ],
- "id": "48691787-3943-49f8-b522-7ebae2e9ba14"
- },
- {
- "cell_type": "code",
- "execution_count": 21,
- "metadata": {
- "outputId": "3eb84b63-0c69-4985-ee9b-d0d69e5ffb33"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_point(filled=True).encode(\n",
- " alt.X('fertility:Q'),\n",
- " alt.Y('life_expect:Q'),\n",
- " alt.Size('pop:Q', scale=alt.Scale(range=[0,1000]),\n",
- " legend=alt.Legend(orient='bottom', titleOrient='left')),\n",
- " alt.Color('cluster:N', legend=None),\n",
- " alt.OpacityValue(0.5),\n",
- " alt.Tooltip('country:N'),\n",
- " alt.Order('pop:Q', sort='descending'),\n",
- " alt.Column('cluster:N')\n",
- ").properties(width=135, height=135)"
- ],
- "id": "29514eee-aa04-452e-af24-1f31af0f5763"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Underneath the hood, the `column` and `row` encodings are translated\n",
- "into a new specification that uses the `facet` view composition\n",
- "operator. We will re-visit faceting in greater depth later on!\n",
- "\n",
- "In the meantime, *can you rewrite the chart above to facet into rows\n",
- "instead of columns?*\n",
- "\n",
- "### A Peek Ahead: Interactive Filtering\n",
- "\n",
- "In later modules, we’ll dive into interaction techniques for data\n",
- "exploration. Here is a sneak peak: binding a range slider to the `year`\n",
- "field to enable interactive scrubbing through each year of data. Don’t\n",
- "worry if the code below is a bit confusing at this point, as we will\n",
- "cover interaction in detail later.\n",
- "\n",
- "*Drag the slider back and forth to see how the data values change over\n",
- "time!*"
- ],
- "id": "86833853-8326-4952-826b-09ca69316390"
- },
- {
- "cell_type": "code",
- "execution_count": 22,
- "metadata": {
- "outputId": "3c934853-9167-4ad1-e560-b366250eb40e"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "select_year = alt.selection_single(\n",
- " name='select', fields=['year'], init={'year': 1955},\n",
- " bind=alt.binding_range(min=1955, max=2005, step=5)\n",
- ")\n",
- "\n",
- "alt.Chart(data).mark_point(filled=True).encode(\n",
- " alt.X('fertility:Q', scale=alt.Scale(domain=[0,9])),\n",
- " alt.Y('life_expect:Q', scale=alt.Scale(domain=[0,90])),\n",
- " alt.Size('pop:Q', scale=alt.Scale(domain=[0, 1200000000], range=[0,1000])),\n",
- " alt.Color('cluster:N', legend=None),\n",
- " alt.OpacityValue(0.5),\n",
- " alt.Tooltip('country:N'),\n",
- " alt.Order('pop:Q', sort='descending')\n",
- ").add_selection(select_year).transform_filter(select_year)"
- ],
- "id": "04fb17df-77f5-4994-8398-bffc8bce9667"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Graphical Marks\n",
- "\n",
- "Our exploration of encoding channels above exclusively uses `point`\n",
- "marks to visualize the data. However, the `point` mark type is only one\n",
- "of the many geometric shapes that can be used to visually represent\n",
- "data. Altair includes a number of built-in mark types, including:\n",
- "\n",
- "- `mark_area()` - Filled areas defined by a top-line and a baseline.\n",
- "- `mark_bar()` - Rectangular bars.\n",
- "- `mark_circle()` - Scatter plot points as filled circles.\n",
- "- `mark_line()` - Connected line segments.\n",
- "- `mark_point()` - Scatter plot points with configurable shapes.\n",
- "- `mark_rect()` - Filled rectangles, useful for heatmaps.\n",
- "- `mark_rule()` - Vertical or horizontal lines spanning the axis.\n",
- "- `mark_square()` - Scatter plot points as filled squares.\n",
- "- `mark_text()` - Scatter plot points represented by text.\n",
- "- `mark_tick()` - Vertical or horizontal tick marks.\n",
- "\n",
- "For a complete list, and links to examples, see the [Altair marks\n",
- "documentation](https://altair-viz.github.io/altair-viz-v4/user_guide/marks.html).\n",
- "Next, we will step through a number of the most commonly used mark types\n",
- "for statistical graphics.\n",
- "\n",
- "### Point Marks\n",
- "\n",
- "The `point` mark type conveys specific points, as in *scatter plots* and\n",
- "*dot plots*. In addition to `x` and `y` encoding channels (to specify 2D\n",
- "point positions), point marks can use `color`, `size`, and `shape`\n",
- "encodings to convey additional data fields.\n",
- "\n",
- "Below is a dot plot of `fertility`, with the `cluster` field redundantly\n",
- "encoded using both the `y` and `shape` channels."
- ],
- "id": "a66c29a1-16bf-487f-8107-84dca728bd34"
- },
- {
- "cell_type": "code",
- "execution_count": 23,
- "metadata": {
- "outputId": "6332a348-f8f0-4dd8-9c4a-63687e286d4a"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_point().encode(\n",
- " alt.X('fertility:Q'),\n",
- " alt.Y('cluster:N'),\n",
- " alt.Shape('cluster:N')\n",
- ")"
- ],
- "id": "cfdda52d-1ccc-42ed-9bbb-00ca8080fa9f"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In addition to encoding channels, marks can be stylized by providing\n",
- "values to the `mark_*()` methods.\n",
- "\n",
- "For example: point marks are drawn with stroked outlines by default, but\n",
- "can be specified to use `filled` shapes instead. Similarly, you can set\n",
- "a default `size` to set the total pixel area of the point mark."
- ],
- "id": "aede0401-03de-4d9e-a898-352f41e809bf"
- },
- {
- "cell_type": "code",
- "execution_count": 24,
- "metadata": {
- "outputId": "dcf26fa9-281b-4297-da50-84c7f5ccd318"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_point(filled=True, size=100).encode(\n",
- " alt.X('fertility:Q'),\n",
- " alt.Y('cluster:N'),\n",
- " alt.Shape('cluster:N')\n",
- ")"
- ],
- "id": "f85d0a35-df76-4e24-a85c-ffcee4c71333"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Circle Marks\n",
- "\n",
- "The `circle` mark type is a convenient shorthand for `point` marks drawn\n",
- "as filled circles."
- ],
- "id": "28e37b38-fc4f-45ff-b45b-fe2958c9a0c8"
- },
- {
- "cell_type": "code",
- "execution_count": 25,
- "metadata": {
- "outputId": "80cd9d0f-c126-4673-bfcf-eaf5b34e0058"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_circle(size=100).encode(\n",
- " alt.X('fertility:Q'),\n",
- " alt.Y('cluster:N'),\n",
- " alt.Shape('cluster:N')\n",
- ")"
- ],
- "id": "61cc7bb8-ab1f-4ddb-9cd1-3b0080525b10"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Square Marks\n",
- "\n",
- "The `square` mark type is a convenient shorthand for `point` marks drawn\n",
- "as filled squares."
- ],
- "id": "0f257da8-8eac-47f2-a2f8-733e7515ef14"
- },
- {
- "cell_type": "code",
- "execution_count": 26,
- "metadata": {
- "outputId": "8ff4b0d4-f3ce-45e5-f597-1a6fd296ba47"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_square(size=100).encode(\n",
- " alt.X('fertility:Q'),\n",
- " alt.Y('cluster:N'),\n",
- " alt.Shape('cluster:N')\n",
- ")"
- ],
- "id": "82b432ee-4700-49fb-ac6b-cb8bc9c16b3c"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Tick Marks\n",
- "\n",
- "The `tick` mark type conveys a data point using a short line segment or\n",
- "“tick”. These are particularly useful for comparing values along a\n",
- "single dimension with minimal overlap. A *dot plot* drawn with tick\n",
- "marks is sometimes referred to as a *strip plot*."
- ],
- "id": "16e8c6f9-cffd-4725-a093-4c46afd3dd98"
- },
- {
- "cell_type": "code",
- "execution_count": 27,
- "metadata": {
- "outputId": "c6133250-333f-4c29-e217-221634dd8337"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_tick().encode(\n",
- " alt.X('fertility:Q'),\n",
- " alt.Y('cluster:N'),\n",
- " alt.Shape('cluster:N')\n",
- ")"
- ],
- "id": "9cfa9190-43e1-4e0f-8132-c2e5c3a78fc4"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Bar Marks\n",
- "\n",
- "The \\`bar\\` mark type draws a rectangle with a position, width, and\n",
- "height.\n",
- "\n",
- "The plot below is a simple bar chart of the population (\\`pop\\`) of each\n",
- "country."
- ],
- "id": "52fdec4c-17bc-49dd-a4db-6644a40aa8a5"
- },
- {
- "cell_type": "code",
- "execution_count": 28,
- "metadata": {
- "outputId": "8da431d3-9ba7-4ecf-de55-e478c4527a39"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_bar().encode(\n",
- " alt.X('country:N'),\n",
- " alt.Y('pop:Q')\n",
- ")"
- ],
- "id": "a57e822a-2289-4d18-bf4f-2ff9aeab7ac2"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The bar width is set to a default size. We will discuss how to adjust\n",
- "the bar width later in this notebook. (A subsequent notebook will take a\n",
- "closer look at configuring axes, scales, and legends.)\n",
- "\n",
- "Bars can also be stacked. Let’s change the `x` encoding to use the\n",
- "`cluster` field, and encode `country` using the `color` channel. We’ll\n",
- "also disable the legend (which would be very long with colors for all\n",
- "countries!) and use tooltips for the country name."
- ],
- "id": "4eaa25d8-ba68-40fa-beb4-69074df8d5eb"
- },
- {
- "cell_type": "code",
- "execution_count": 29,
- "metadata": {
- "outputId": "7960be03-eefd-4c3f-a114-8405395c772c"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_bar().encode(\n",
- " alt.X('cluster:N'),\n",
- " alt.Y('pop:Q'),\n",
- " alt.Color('country:N', legend=None),\n",
- " alt.Tooltip('country:N')\n",
- ")"
- ],
- "id": "df09d315-04d8-47ef-bd20-737ff0601953"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In the chart above, the use of the `color` encoding channel causes\n",
- "Altair / Vega-Lite to automatically stack the bar marks. Otherwise, bars\n",
- "would be drawn on top of each other! Try adding the parameter\n",
- "`stack=None` to the `y` encoding channel to see what happens if we don’t\n",
- "apply stacking…\n",
- "\n",
- "The examples above create bar charts from a zero-baseline, and the `y`\n",
- "channel only encodes the non-zero value (or height) of the bar. However,\n",
- "the bar mark also allows you to specify starting and ending points to\n",
- "convey ranges.\n",
- "\n",
- "The chart below uses the `x` (starting point) and `x2` (ending point)\n",
- "channels to show the range of life expectancies within each regional\n",
- "cluster. Below we use the `min` and `max` aggregation functions to\n",
- "determine the end points of the range; we will discuss aggregation in\n",
- "greater detail in the next notebook!\n",
- "\n",
- "Alternatively, you can use `x` and `width` to provide a starting point\n",
- "plus offset, such that `x2 = x + width`."
- ],
- "id": "e84e49e9-1d25-4fcb-9516-843f40ab0cef"
- },
- {
- "cell_type": "code",
- "execution_count": 30,
- "metadata": {
- "outputId": "2fa67514-b66c-4449-a1e3-c0b1b377ed3a"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data2000).mark_bar().encode(\n",
- " alt.X('min(life_expect):Q'),\n",
- " alt.X2('max(life_expect):Q'),\n",
- " alt.Y('cluster:N')\n",
- ")"
- ],
- "id": "9249052a-d7bb-4505-8565-9d1a2979549c"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Line Marks\n",
- "\n",
- "The `line` mark type connects plotted points with line segments, for\n",
- "example so that a line’s slope conveys information about the rate of\n",
- "change.\n",
- "\n",
- "Let’s plot a line chart of fertility per country over the years, using\n",
- "the full, unfiltered global development data frame. We’ll again hide the\n",
- "legend and use tooltips instead."
- ],
- "id": "68fe8e75-e4d4-4254-9a67-2c6e4c504ede"
- },
- {
- "cell_type": "code",
- "execution_count": 31,
- "metadata": {
- "outputId": "7bbd15a9-4b8f-4f66-fe7e-6a55f2c38449"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data).mark_line().encode(\n",
- " alt.X('year:O'),\n",
- " alt.Y('fertility:Q'),\n",
- " alt.Color('country:N', legend=None),\n",
- " alt.Tooltip('country:N')\n",
- ").properties(\n",
- " width=400\n",
- ")"
- ],
- "id": "e777bacc-6f85-4887-a26a-7ca8324c1267"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "We can see interesting variations per country, but overall trends for\n",
- "lower numbers of children per family over time. Also note that we set a\n",
- "custom width of 400 pixels. *Try changing (or removing) the widths and\n",
- "see what happens!*\n",
- "\n",
- "Let’s change some of the default mark parameters to customize the plot.\n",
- "We can set the `strokeWidth` to determine the thickness of the lines and\n",
- "the `opacity` to add some transparency. By default, the `line` mark uses\n",
- "straight line segments to connect data points. In some cases we might\n",
- "want to smooth the lines. We can adjust the interpolation used to\n",
- "connect data points by setting the `interpolate` mark parameter. Let’s\n",
- "use `'monotone'` interpolation to provide smooth lines that are also\n",
- "guaranteed not to inadvertently generate “false” minimum or maximum\n",
- "values as a result of the interpolation."
- ],
- "id": "03d335a8-f70f-4b5e-b39c-021a258100f9"
- },
- {
- "cell_type": "code",
- "execution_count": 32,
- "metadata": {
- "outputId": "07007338-a2c7-4dc2-9f36-bb344e4103ec"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(data).mark_line(\n",
- " strokeWidth=3,\n",
- " opacity=0.5,\n",
- " interpolate='monotone'\n",
- ").encode(\n",
- " alt.X('year:O'),\n",
- " alt.Y('fertility:Q'),\n",
- " alt.Color('country:N', legend=None),\n",
- " alt.Tooltip('country:N')\n",
- ").properties(\n",
- " width=400\n",
- ")"
- ],
- "id": "1802cb26-10d6-4684-896d-46ed2aa97587"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The `line` mark can also be used to create *slope graphs*, charts that\n",
- "highlight the change in value between two comparison points using line\n",
- "slopes.\n",
- "\n",
- "Below let’s create a slope graph comparing the populations of each\n",
- "country at minimum and maximum years in our full dataset: 1955 and 2005.\n",
- "We first create a new Pandas data frame filtered to those years, then\n",
- "use Altair to create the slope graph.\n",
- "\n",
- "By default, Altair places the years close together. To better space out\n",
- "the years along the x-axis, we can indicate the size (in pixels) of\n",
- "discrete steps along the width of our chart as indicated by the comment\n",
- "below. Try adjusting the width `step` value below and see how the chart\n",
- "changes in response."
- ],
- "id": "3a45ab6f-b340-405d-a135-c77bcb40513d"
- },
- {
- "cell_type": "code",
- "execution_count": 33,
- "metadata": {
- "outputId": "edd1292a-97a7-44d1-b2ec-c5b8d755aa86"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "dataTime = data.loc[(data['year'] == 1955) | (data['year'] == 2005)]\n",
- "\n",
- "alt.Chart(dataTime).mark_line(opacity=0.5).encode(\n",
- " alt.X('year:O'),\n",
- " alt.Y('pop:Q'),\n",
- " alt.Color('country:N', legend=None),\n",
- " alt.Tooltip('country:N')\n",
- ").properties(\n",
- " width={\"step\": 50} # adjust the step parameter\n",
- ")"
- ],
- "id": "0fe3a789-11fc-45cc-b510-d1fff51000fe"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Area Marks\n",
- "\n",
- "The `area` mark type combines aspects of `line` and `bar` marks: it\n",
- "visualizes connections (slopes) among data points, but also shows a\n",
- "filled region, with one edge defaulting to a zero-valued baseline.\n",
- "\n",
- "The chart below is an area chart of population over time for just the\n",
- "United States:"
- ],
- "id": "e98f6b7e-4d34-41bc-b1f0-6c1846bb1feb"
- },
- {
- "cell_type": "code",
- "execution_count": 34,
- "metadata": {
- "outputId": "37cd899d-2ad1-42ea-fbe0-12e591a28326"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "dataUS = data.loc[data['country'] == 'United States']\n",
- "\n",
- "alt.Chart(dataUS).mark_area().encode(\n",
- " alt.X('year:O'),\n",
- " alt.Y('fertility:Q')\n",
- ")"
- ],
- "id": "80cd4a15-08f4-4f0c-9e9c-822203843861"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Similar to `line` marks, `area` marks support an `interpolate`\n",
- "parameter."
- ],
- "id": "973753f5-fe0d-41c2-b278-6fbee571a233"
- },
- {
- "cell_type": "code",
- "execution_count": 35,
- "metadata": {
- "outputId": "eba5baab-44be-46ac-c9ae-0ad3b094573a"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(dataUS).mark_area(interpolate='monotone').encode(\n",
- " alt.X('year:O'),\n",
- " alt.Y('fertility:Q')\n",
- ")"
- ],
- "id": "6e674da5-5188-40f3-bad0-1a8305861ebb"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Similar to `bar` marks, `area` marks also support stacking. Here we\n",
- "create a new data frame with data for the three North American\n",
- "countries, then plot them using an `area` mark and a `color` encoding\n",
- "channel to stack by country."
- ],
- "id": "c4af871e-3f17-4094-89a0-650ce683def0"
- },
- {
- "cell_type": "code",
- "execution_count": 36,
- "metadata": {
- "outputId": "70e210aa-4771-4ed9-e5a3-0af587d03c60"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "dataNA = data.loc[\n",
- " (data['country'] == 'United States') |\n",
- " (data['country'] == 'Canada') |\n",
- " (data['country'] == 'Mexico')\n",
- "]\n",
- "\n",
- "alt.Chart(dataNA).mark_area().encode(\n",
- " alt.X('year:O'),\n",
- " alt.Y('pop:Q'),\n",
- " alt.Color('country:N')\n",
- ")"
- ],
- "id": "d0711c43-22a8-4fcb-8074-f3f7993dd021"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "By default, stacking is performed relative to a zero baseline. However,\n",
- "other `stack` options are available:\n",
- "\n",
- "- `center` - to stack relative to a baseline in the center of the\n",
- " chart, creating a *streamgraph* visualization, and\n",
- "- `normalize` - to normalize the summed data at each stacking point to\n",
- " 100%, enabling percentage comparisons.\n",
- "\n",
- "Below we adapt the chart by setting the `y` encoding `stack` attribute\n",
- "to `center`. What happens if you instead set it `normalize`?"
- ],
- "id": "882f1e16-c660-44cf-bf22-d8534b1818e3"
- },
- {
- "cell_type": "code",
- "execution_count": 37,
- "metadata": {
- "outputId": "3a7cb75a-3acf-4b0e-d0e8-cdc7c85fd5ee"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(dataNA).mark_area().encode(\n",
- " alt.X('year:O'),\n",
- " alt.Y('pop:Q', stack='center'),\n",
- " alt.Color('country:N')\n",
- ")"
- ],
- "id": "18b7aa73-e5e4-4e7a-b45b-3ea00771c47a"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "To disable stacking altogether, set the `stack` attribute to `None`. We\n",
- "can also add `opacity` as a default mark parameter to ensure we see the\n",
- "overlapping areas!"
- ],
- "id": "42a46d4c-add1-4992-8a82-8d88032d1e4a"
- },
- {
- "cell_type": "code",
- "execution_count": 38,
- "metadata": {
- "outputId": "41345e53-eeaa-4c69-969d-738c1479ba26"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(dataNA).mark_area(opacity=0.5).encode(\n",
- " alt.X('year:O'),\n",
- " alt.Y('pop:Q', stack=None),\n",
- " alt.Color('country:N')\n",
- ")"
- ],
- "id": "81f3ad39-4ca5-4d6c-8c5a-6dbe2cf6039a"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The `area` mark type also supports data-driven baselines, with both the\n",
- "upper and lower series determined by data fields. As with `bar` marks,\n",
- "we can use the `x` and `x2` (or `y` and `y2`) channels to provide end\n",
- "points for the area mark.\n",
- "\n",
- "The chart below visualizes the range of minimum and maximum fertility,\n",
- "per year, for North American countries:"
- ],
- "id": "62768583-aa86-4ce8-b348-87a6fea12100"
- },
- {
- "cell_type": "code",
- "execution_count": 39,
- "metadata": {
- "outputId": "fb6d0868-79f4-4f96-8f5d-aff6d504b3fe"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(dataNA).mark_area().encode(\n",
- " alt.X('year:O'),\n",
- " alt.Y('min(fertility):Q'),\n",
- " alt.Y2('max(fertility):Q')\n",
- ").properties(\n",
- " width={\"step\": 40}\n",
- ")"
- ],
- "id": "89219037-98e9-4276-ab79-8aa617e35658"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "We can see a larger range of values in 1995, from just under 4 to just\n",
- "under 7. By 2005, both the overall fertility values and the variability\n",
- "have declined, centered around 2 children per familty.\n",
- "\n",
- "All the `area` mark examples above use a vertically oriented area.\n",
- "However, Altair and Vega-Lite support horizontal areas as well. Let’s\n",
- "transpose the chart above, simply by swapping the `x` and `y` channels."
- ],
- "id": "6ea2faba-3462-4acb-9783-97d8dd99bc66"
- },
- {
- "cell_type": "code",
- "execution_count": 40,
- "metadata": {
- "outputId": "e7bf35e5-c94b-4316-9f8d-0dc68f242763"
- },
- "outputs": [
- {
- "output_type": "display_data",
- "metadata": {},
- "data": {
- "text/html": [
- "\n",
- "\n",
- ""
- ]
- }
- }
- ],
- "source": [
- "alt.Chart(dataNA).mark_area().encode(\n",
- " alt.Y('year:O'),\n",
- " alt.X('min(fertility):Q'),\n",
- " alt.X2('max(fertility):Q')\n",
- ").properties(\n",
- " width={\"step\": 40}\n",
- ")"
- ],
- "id": "be15d7ba-5fb8-48d5-a80a-96ade3cfbd6a"
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Summary\n",
- "\n",
- "We’ve completed our tour of data types, encoding channels, and graphical\n",
- "marks! You should now be well-equipped to further explore the space of\n",
- "encodings, mark types, and mark parameters. For a comprehensive\n",
- "reference – including features we’ve skipped over here! – see the Altair\n",
- "[marks](https://altair-viz.github.io/altair-viz-v4/user_guide/marks.html)\n",
- "and\n",
- "[encoding](https://altair-viz.github.io/altair-viz-v4/user_guide/encoding.html)\n",
- "documentation.\n",
- "\n",
- "In the next module, we will look at the use of data transformations to\n",
- "create charts that summarize data or visualize new derived fields. In a\n",
- "later module, we’ll examine how to further customize your charts by\n",
- "modifying scales, axes, and legends.\n",
- "\n",
- "Interested in learning more about visual encoding?\n",
- "\n",
- "![](\"https://cdn-images-1.medium.com/max/2000/1*jsb78Rr2cDy6zrE7j2IKig.png\" "\\"Bertin's")
\n",
- "\n",
- "Bertin’s taxonomy of visual encodings from\n",
- "Sémiologie\n",
- "Graphique, as adapted by\n",
- "Mike Bostock.\n",
- "\n",
- "- The systematic study of marks, visual encodings, and backing data\n",
- " types was initiated by [Jacques\n",
- " Bertin](https://en.wikipedia.org/wiki/Jacques_Bertin) in his\n",
- " pioneering 1967 work [*Sémiologie Graphique (The Semiology of\n",
- " Graphics)*](https://books.google.com/books/about/Semiology_of_Graphics.html?id=X5caQwAACAAJ).\n",
- " The image above illustrates position, size, value (brightness),\n",
- " texture, color (hue), orientation, and shape channels, alongside\n",
- " Bertin’s recommendations for the data types they support.\n",
- "- The framework of data types, marks, and channels also guides\n",
- " *automated* visualization design tools, starting with [Mackinlay’s\n",
- " APT (A Presentation\n",
- " Tool)](https://scholar.google.com/scholar?cluster=10191273548472217907)\n",
- " in 1986 and continuing in more recent systems such as\n",
- " [Voyager](http://idl.cs.washington.edu/papers/voyager/) and\n",
- " [Draco](http://idl.cs.washington.edu/papers/draco/).\n",
- "- The identification of nominal, ordinal, interval, and ratio types\n",
- " dates at least as far back as S. S. Steven’s 1947 article [*On the\n",
- " theory of scales of\n",
- " measurement*](https://scholar.google.com/scholar?cluster=14356809180080326415)."
- ],
- "id": "c7a1b05c-55d2-4563-9bf7-6ec4d95e7c12"
- }
- ],
- "nbformat": 4,
- "nbformat_minor": 5,
- "metadata": {
- "kernelspec": {
- "name": "python3",
- "display_name": "Python 3 (ipykernel)",
- "language": "python"
- },
- "language_info": {
- "name": "python",
- "codemirror_mode": {
- "name": "ipython",
- "version": "3"
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython3",
- "version": "3.11.1"
- }
- }
-}
\ No newline at end of file
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--- a/lartpy-blog-post.ipynb
+++ b/src/blog/posts/.ipynb_checkpoints/lartpy-checkpoint.ipynb
@@ -1 +1,573 @@
-{"cells":[{"cell_type":"markdown","metadata":{"tags":[],"cell_id":"74580f134ddc410bafde8c5caffa5364","deepnote_cell_type":"markdown"},"source":"# L'art pour l'art: creating generative art with L-systems in Python\n\n\n\n[Creative coding](https://en.wikipedia.org/wiki/Creative_coding) is fun if you know a thing or two about programming. And if, like me, you are an utter noob when it comes to brushes and pencils, then it is even more enticing as a means to express yourself and create something just for the sake of it. It doesn't have to be functional, but you do get to hone your hacking skills and set challenges for yourself along the way.\n\nA fellow data scientist who is into [\"Art & AI\"](https://www.basbloemberg.nl/) recently pointed me to the field of [generative art](https://aiartists.org/generative-art-design). I have always been facinated by [emergence](https://en.wikipedia.org/wiki/Emergence) and even more so when I came across the picture above. It is featured in [this blog](https://g-e-n-a-r-t.com/en/post.php?p=10) on how to draw a pencil-sketch-like forest with Processing. One thing led to another: I had a go at [Processing in Python mode](https://py.processing.org/tutorials/command-line/), dabbled with [matplotlib for animations](http://louistiao.me/posts/notebooks/embedding-matplotlib-animations-in-jupyter-as-interactive-javascript-widgets/) and read Schiffman's [the Nature of Code](https://natureofcode.com/book/).\n\n_\"Would it be possible to create a Python project that can generate those pencil-like drawings with random forests, with different types of trees?\"_, I thought (pun intended). Of course, someone already thought of that and it even has a name: __algorithmic botany__. Przemyslaw Prusinkiewicz and Aristid Lindenmayer wrote the seminal book on the subject in 1990, [The Algorithmic Beauty of Plants](http://algorithmicbotany.org/papers/#abop). Lindenmayer invented [L-systems](https://en.wikipedia.org/wiki/L-system) already back in 1968. Today, household computers have enough resources to handle large-ish parallel writing systems and you could start modelling the growth of any plant using a framework like [L-Py](https://lpy.readthedocs.io/en/latest/).\n\nAlthough a lot has been written on the subject and there are quite a few open source libraries, they weren't quite what I have in mind. Instead, the idea of creating generative art in Python emerged using the following components:\n\n1. A lightweight implementation of L-systems that also supports stochastic and parametric production rules;\n2. Integration with [p5js](https://p5js.org) via [pyp5js](https://berinhard.github.io/pyp5js/) as a web-native graphing engine.\n\nThe possibilities are endless and I can foresee spending way too much time on this. In this blog post, I will lay out the ideas behind this approach.","block_group":"74580f134ddc410bafde8c5caffa5364"},{"cell_type":"markdown","metadata":{"tags":[],"cell_id":"ce3bd52d4200405b8184949d70c08cd0","deepnote_cell_type":"markdown"},"source":"# Playing with L-systems in Python\n\nThere are different kinds of L-systems, with increasing complexity. We will start with the simplest: Lindenmayer's original L-system for modelling the growth of algae (We will jump right in, please read the [article on Wikipedia](https://en.wikipedia.org/wiki/L-system) if you need more context).\n\n## D0L: deterministic context-free L-system\n","block_group":"ce3bd52d4200405b8184949d70c08cd0"},{"cell_type":"code","metadata":{"tags":[],"cell_id":"4f89aef0f75d4aa3808305b92a4925d3","source_hash":"8b352d4c","execution_start":1619612317163,"execution_millis":21,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"source":"# define L-system\nAXIOM = 'A'\nRULES = {'A': 'AB',\n 'B': 'A'}\n\n\n# initialize \nproductions = [AXIOM]\niterations = 7\n\n\ndef generate_d0l(axiom, productions, iterations):\n def rewrite_l(word):\n productions.append(''.join([RULES.get(c) or c for c in word]))\n return productions[-1]\n\n\n if iterations == 0:\n return axiom\n else:\n return rewrite_l(generate_d0l(axiom, productions, iterations - 1))\n\n\n# main\ngenerate_d0l(AXIOM, productions, iterations)\nprint(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))","block_group":"4f89aef0f75d4aa3808305b92a4925d3","execution_count":null,"outputs":[{"name":"stdout","text":"0: A\n1: AB\n2: ABA\n3: ABAAB\n4: ABAABABA\n5: ABAABABAABAAB\n6: ABAABABAABAABABAABABA\n7: ABAABABAABAABABAABABAABAABABAABAAB\n\n","output_type":"stream"}]},{"cell_type":"markdown","metadata":{"tags":[],"cell_id":"0abb04548758427aa75800c3d3fb8ae3","deepnote_cell_type":"markdown"},"source":"I actually found the recursive Python implementation on this [introductory website on recursion](https://understanding-recursion.readthedocs.io/en/latest/16%20L-System%20Solution.html). While I still struggle to apply recursion, I find it satisfying to solve coding problems this way. And even with just these twenty lines of code, we have already stumbled on the [Fibonacci numbers](https://en.wikipedia.org/wiki/Fibonacci_number)! Have a look at the length of each successive sequence:\n","block_group":"0abb04548758427aa75800c3d3fb8ae3"},{"cell_type":"code","metadata":{"tags":[],"cell_id":"7c9e0ab688d543ddb427e0706d09d8c1","source_hash":"8264db4e","is_code_hidden":true,"execution_start":1619612317215,"execution_millis":135,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"source":"print([len(word) for word in productions])","block_group":"7c9e0ab688d543ddb427e0706d09d8c1","execution_count":null,"outputs":[{"name":"stdout","text":"[1, 2, 3, 5, 8, 13, 21, 34]\n","output_type":"stream"}]},{"cell_type":"markdown","metadata":{"tags":[],"cell_id":"2c2bc972bb9c4fcba319367e675ad756","deepnote_cell_type":"markdown"},"source":"Awesome as the nature of code may be, we are still a long way off from actually generating a tree. For that, we need branching rules. To do so, basic L-systems also allow constants, which are left untouched by the production rules. It is common to add constants `+` and `-` to denote rotations when branching, and `[`,`]` for handling the locations of the branching points. For a fractal plant, the code is as follows:","block_group":"2c2bc972bb9c4fcba319367e675ad756"},{"cell_type":"code","metadata":{"tags":[],"cell_id":"0edc13f7a3a94a8f8c6d39e03e99b6dd","source_hash":"b4945e20","execution_start":1619612317216,"execution_millis":134,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"source":"AXIOM = \"X\"\nRULES = {\"X\": \"F+[[X]-X]-F[-FX]+X\",\n \"F\": \"FF\"}\nproductions = [AXIOM]\ngenerate_d0l(AXIOM, productions, iterations)\nprint(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))","block_group":"0edc13f7a3a94a8f8c6d39e03e99b6dd","execution_count":null,"outputs":[{"name":"stdout","text":"0: X\n1: F+[[X]-X]-F[-FX]+X\n2: FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X\n3: FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X\n4: FFFFFFFF+[[FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFFFFFF[-FFFFFFFFFFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X\n5: 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is amazing to see how complexity increases by adding slightly longer rules. To actually draw something, we translate the letters as follows:\n* \"F\" means \"draw forward\"\n* \"-\" means \"turn right\", using a predefined value e.g. 30°\n* \"+\" means \"turn left 30°\"\n* \"X\" does not correspond to any drawing action and is used to control the evolution of the curve.\n\nThe square bracket \"\\[\" corresponds to saving the current values for position and angle, which are restored when the corresponding \"]\" is executed, which effectively is a [LIFO stack](https://en.wikipedia.org/wiki/Stack_(abstract_data_type)). We will go into the details of how to draw later.","block_group":"aa7ef8890e03437da0f5ea9bb687cb59"},{"cell_type":"markdown","metadata":{"tags":[],"cell_id":"cedfb378ff2b437c947fd884ee69bed5","source_hash":"fdd41db5","execution_start":1619388009090,"execution_millis":35,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"markdown"},"source":"## Adding stochastic rules\n\nD0L systems are completely deterministic, that is, each starting axiom yields the same result. Using this to draw a forest would result in a boring scene: all trees would be identical. To mimic mutations in nature, stochastic L-systems allow the same letter to have for different production rules with a given probability. For example, if we want three different production rules for F with equal probability\n\n```\np1: F(0.33) → F[+F]F[−F]F\np2: F(0.33) → F[+F]F\np3: F(0.34) → F[−F]F\n```\n\nthe Python implementation could look something like this:","block_group":"cedfb378ff2b437c947fd884ee69bed5"},{"cell_type":"code","metadata":{"tags":[],"cell_id":"4e3895f0f15b431a9489742b3f7cd84f","source_hash":"77e3defc","execution_start":1619612508337,"execution_millis":10,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"source":"from numpy.random import default_rng\n\nAXIOM = \"F\"\nRULES = {\"F\": [\"F[+F]F[−F]F\", \"F[+F]F\", \"F[−F]F\"]}\nproductions = [AXIOM]\niterations = 3\n\n\nrng = default_rng()\ndef generate_stochastic(axiom, productions, iterations):\n def get_stochastic_rule(letter):\n if letter not in RULES.keys():\n return letter\n else:\n return RULES.get(letter)[rng.choice(3,1)[0]]\n\n\n def rewrite_l(word):\n productions.append(''.join([get_stochastic_rule(c) for c in word]))\n return productions[-1]\n\n\n if iterations == 0:\n return axiom\n else:\n return rewrite_l(generate_stochastic(axiom, productions, iterations - 1))\n\n\ngenerate_stochastic(AXIOM, productions, iterations)\nprint(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))","block_group":"4e3895f0f15b431a9489742b3f7cd84f","execution_count":null,"outputs":[{"name":"stdout","text":"0: F\n1: F[−F]F\n2: F[−F]F[−F[−F]F]F[−F]F\n3: F[−F]F[−F[−F]F]F[−F]F[−F[−F]F[−F[+F]F]F[+F]F[−F]F]F[+F]F[−F[+F]F[−F]F]F[+F]F[−F]F\n\n","output_type":"stream"}]},{"cell_type":"markdown","metadata":{"tags":[],"cell_id":"ed6a867aa5884874b555f482c88a9e5f","deepnote_cell_type":"markdown"},"source":"Here's another run with a different result:","block_group":"ed6a867aa5884874b555f482c88a9e5f"},{"cell_type":"code","metadata":{"tags":[],"cell_id":"ec7650359b644649a843d7a30e0ce467","source_hash":"32960fdd","is_code_hidden":true,"execution_start":1619612520082,"execution_millis":0,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"source":"# show that a new run generates different result\nproductions = [AXIOM]\ngenerate_stochastic(AXIOM, productions, iterations)\nprint(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))","block_group":"ec7650359b644649a843d7a30e0ce467","execution_count":null,"outputs":[{"name":"stdout","text":"0: F\n1: F[+F]F[−F]F\n2: F[+F]F[−F]F[+F[+F]F]F[−F]F[−F[+F]F[−F]F]F[+F]F[−F]F\n3: F[−F]F[+F[+F]F]F[+F]F[−F[+F]F]F[+F]F[−F]F[+F[−F]F[+F[+F]F]F[−F]F]F[+F]F[−F[+F]F[−F]F]F[+F]F[−F]F[−F[−F]F[+F[−F]F]F[−F]F[−F[+F]F]F[+F]F[−F]F]F[+F]F[−F]F[+F[+F]F[−F]F]F[−F]F[−F[+F]F[−F]F]F[+F]F[−F]F\n\n","output_type":"stream"}]},{"cell_type":"markdown","metadata":{"tags":[],"cell_id":"4d37ba2098994f79a57b03abb2e8fb71","deepnote_cell_type":"markdown"},"source":"## Adding parameters\n\nIn a parametric L-system, letters are allowed to have parameters, which correspond with formal parameters used in the specification of L-system productions. This can be used to model _Anabaena catenula_ (taken from [Hanan's dissertation](http://algorithmicbotany.org/papers/hanan.dis1992.html)):","block_group":"4d37ba2098994f79a57b03abb2e8fb71"},{"cell_type":"code","metadata":{"tags":[],"cell_id":"ffbb155396f541bea91cdddafa44a742","source_hash":"ddba2700","execution_start":1619612317279,"execution_millis":71,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"source":"from collections import namedtuple\n\n\n# parameters\nF = namedtuple('F', ['s', 't', 'o']) # parameterized cell\ns = {2: \"AS\", 1: \"BS\"} # cell size\nt = {1: \"A\", 2: \"B\"} # cell type\no = {1: \"right\", -1: \"left\"} # cell orientation\n\nAXIOM = [F(1, 2, 1)]\nRULES = {F(2,1,1): [F(2,1,-1), F(1,2,1)],\n F(2,1,-1): [F(1,2,-1), F(2,1,1)],\n F(1,2,1): [F(2,1,1)],\n F(1,2,-1): [F(2,1,-1)],\n }\nproductions = [AXIOM]\niterations = 5\n\n\ndef unnest(list_, unnested_=None):\n \"\"\"Utility function to unnest arbitrarily deep list of lists\n \"\"\"\n if unnested_ is None:\n unnested_ = []\n for x in list_:\n if not isinstance(x, list):\n unnested_.append(x)\n if isinstance(x, list):\n unnest(x, unnested_)\n return unnested_\n\n\ndef generate_parametric(axiom, productions, iterations):\n def rewrite_l(word):\n productions.append(unnest([RULES.get(c) or c for c in unnest(word)]))\n return productions[-1]\n\n\n if iterations == 0:\n return [axiom]\n else:\n return rewrite_l(generate_parametric(axiom, productions, iterations - 1))\n\n\ngenerate_parametric(AXIOM, productions, iterations)\nprint(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))","block_group":"ffbb155396f541bea91cdddafa44a742","execution_count":null,"outputs":[{"name":"stdout","text":"0: [F(s=1, t=2, o=1)]\n1: [F(s=2, t=1, o=1)]\n2: [F(s=2, t=1, o=-1), F(s=1, t=2, o=1)]\n3: [F(s=1, t=2, o=-1), F(s=2, t=1, o=1), F(s=2, t=1, o=1)]\n4: [F(s=2, t=1, o=-1), F(s=2, t=1, o=-1), F(s=1, t=2, o=1), F(s=2, t=1, o=-1), F(s=1, t=2, o=1)]\n5: [F(s=1, t=2, o=-1), F(s=2, t=1, o=1), F(s=1, t=2, o=-1), F(s=2, t=1, o=1), F(s=2, t=1, o=1), F(s=1, t=2, o=-1), F(s=2, t=1, o=1), F(s=2, t=1, o=1)]\n\n","output_type":"stream"}]},{"cell_type":"markdown","metadata":{"tags":[],"cell_id":"c81bb3c6722640deb2d8b5e2a7a35fdb","deepnote_cell_type":"markdown"},"source":"\nWhile the _Anabaena_ example above only makes simple comparisons, parametric L-systems can use any expression using the parameters in combination with the arithmetic operators +, −, ∗, /; the exponentiation operator ∧, the relational operators <, >, =; the logical operators !, &, | (not, and, or) etc. For example, we could define a parameter `time` which increases with every iteration. This could be used to thicken the width of a branch of a tree.\n","block_group":"c81bb3c6722640deb2d8b5e2a7a35fdb"},{"cell_type":"markdown","metadata":{"tags":[],"cell_id":"3153eb8d46394822906ac6430be06f3c","source_hash":"616536f3","execution_start":1619387455407,"execution_millis":7,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"markdown"},"source":"# Using pyp5js for Pythonic drawing on the web\n\nWhen Lindenmayer devised the L-system, [Logo](https://en.wikipedia.org/wiki/Logo_(programming_language)) was one of the few programming langauges available. It included [turtle graphics](https://en.wikipedia.org/wiki/Turtle_graphics) and thus the basis of algorithmic art was born by translating the alphabet of an L-system to turtle commands. The examples from the Nature of Code have in fact [implemented this in Processing](https://github.com/nature-of-code/noc-examples-processing/blob/master/chp08_fractals/NOC_8_09_LSystem/Turtle.pde). But rather than constrain yourself to the desktop, more mileage can be had by using [p5js](https://p5js.org) which is \"... an interpretation of Processing for today's web\". To demonstrate, take the following example:","block_group":"3153eb8d46394822906ac6430be06f3c"},{"cell_type":"code","metadata":{"tags":[],"cell_id":"339bc90f77ba4f03ae639db0ba417ad8","source_hash":"cbe4ac7d","execution_start":1619612317283,"execution_millis":73,"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"source":"AXIOM = 'G'\nRULES = {\n 'F': 'FF',\n 'G': 'F-[[G]+G]+F[+FG]-G'\n}\nproductions = [AXIOM]\ngenerate_d0l(AXIOM, productions, iterations=5)\nprint(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))","block_group":"339bc90f77ba4f03ae639db0ba417ad8","execution_count":null,"outputs":[{"name":"stdout","text":"0: G\n1: F-[[G]+G]+F[+FG]-G\n2: FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G\n3: FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G\n4: 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Rizo has already implemented L-systems in p5js, available on [thefractal.zone](https://thefractal.zone/). Copying the axiom and rules, and setting the branching angle $\\theta$ to 30°, yields the drawing below. Note that the code only shows 5 iterations, while the drawing is based on more iterations (I have put the slider on maximum). When using recursion in Python you may quickly hit a limit: as I tried to execute `iterations=10` on a standard VM, Deepnote threw an error `IOPub data rate exceeded`. Yet another challenge to read-up and use [tail-call optimization in Python](https://sagnibak.github.io/blog/python-is-haskell-tail-recursion/).","block_group":"0ca8b0c2a4124b53bed66534c630dcb6"},{"cell_type":"markdown","metadata":{"tags":[],"cell_id":"68975c6e2ce94299841975cedbb1626a","deepnote_cell_type":"markdown"},"source":"","block_group":"68975c6e2ce94299841975cedbb1626a"},{"cell_type":"markdown","metadata":{"tags":[],"cell_id":"ab0730498f754a9497120d0e9a5a78a4","deepnote_cell_type":"markdown"},"source":"Having covered the algorithmic and technical components, we can now start bringing it all together. There are still quite a few things to experiment with in order to produce realistic sketches, such as adding noise to draw 'sketchy' lines, adding thickness to branches, adding shadows with brightness off-sets and composing a scene with overlaying trees. As a Pythonista I was happy to find [pyp5js](https://berinhard.github.io/pyp5js/), which allows you to re-use the ideas of Processing in Python, and transcoding it to p5.js using Transcrypt. It covers all the methods from p5.js and gives us enough drawing tools to play with. But that's for another post. For now, I will leave you with a [generative creation from Anders Hoff](https://inconvergent.net/generative/) which may inspire you to start creating generative art in Python, too.\n\n","block_group":"ab0730498f754a9497120d0e9a5a78a4"},{"cell_type":"markdown","metadata":{"tags":[],"cell_id":"afcb48bd1c7848d2969a63a51df32886","deepnote_cell_type":"markdown"},"source":"","block_group":"afcb48bd1c7848d2969a63a51df32886"},{"cell_type":"markdown","source":"\n
\nCreated in Deepnote","metadata":{"created_in_deepnote_cell":true,"deepnote_cell_type":"markdown"}}],"nbformat":4,"nbformat_minor":0,"metadata":{"deepnote":{"is_reactive":false},"orig_nbformat":2,"deepnote_notebook_id":"94e2a17bd9324e6db3fff66e4a015929","deepnote_execution_queue":[]}}
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+{
+ "cells": [
+ {
+ "cell_type": "raw",
+ "metadata": {
+ "tags": []
+ },
+ "source": [
+ "---\n",
+ "title: L'art pour l'art: creating generative art with L-systems in Python\n",
+ "subtitle: Some experiments on the algorithmic beauty of plants\n",
+ "description: \"Would it be possible to create a Python project that can generate those pencil-like drawings with random forests, with different types of trees?\", I thought (pun intended). Of course, someone already thought of that and it even has a name: algorithmic botany.\n",
+ "date: 2021-04-26\n",
+ "date-format: short\n",
+ "image: /images/lartpy.jpg\n",
+ "categories: [english, visualization, generative art]\n",
+ "---"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "74580f134ddc410bafde8c5caffa5364",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "# L'art pour l'art: creating generative art with L-systems in Python\n",
+ "\n",
+ "\n",
+ "\n",
+ "[Creative coding](https://en.wikipedia.org/wiki/Creative_coding) is fun if you know a thing or two about programming. And if, like me, you are an utter noob when it comes to brushes and pencils, then it is even more enticing as a means to express yourself and create something just for the sake of it. It doesn't have to be functional, but you do get to hone your hacking skills and set challenges for yourself along the way.\n",
+ "\n",
+ "A fellow data scientist who is into [\"Art & AI\"](https://www.basbloemberg.nl/) recently pointed me to the field of [generative art](https://aiartists.org/generative-art-design). I have always been facinated by [emergence](https://en.wikipedia.org/wiki/Emergence) and even more so when I came across the picture above. It is featured in [this blog](https://g-e-n-a-r-t.com/en/post.php?p=10) on how to draw a pencil-sketch-like forest with Processing. One thing led to another: I had a go at [Processing in Python mode](https://py.processing.org/tutorials/command-line/), dabbled with [matplotlib for animations](http://louistiao.me/posts/notebooks/embedding-matplotlib-animations-in-jupyter-as-interactive-javascript-widgets/) and read Schiffman's [the Nature of Code](https://natureofcode.com/book/).\n",
+ "\n",
+ "_\"Would it be possible to create a Python project that can generate those pencil-like drawings with random forests, with different types of trees?\"_, I thought (pun intended). Of course, someone already thought of that and it even has a name: __algorithmic botany__. Przemyslaw Prusinkiewicz and Aristid Lindenmayer wrote the seminal book on the subject in 1990, [The Algorithmic Beauty of Plants](http://algorithmicbotany.org/papers/#abop). Lindenmayer invented [L-systems](https://en.wikipedia.org/wiki/L-system) already back in 1968. Today, household computers have enough resources to handle large-ish parallel writing systems and you could start modelling the growth of any plant using a framework like [L-Py](https://lpy.readthedocs.io/en/latest/).\n",
+ "\n",
+ "Although a lot has been written on the subject and there are quite a few open source libraries, they weren't quite what I have in mind. Instead, the idea of creating generative art in Python emerged using the following components:\n",
+ "\n",
+ "1. A lightweight implementation of L-systems that also supports stochastic and parametric production rules;\n",
+ "2. Integration with [p5js](https://p5js.org) via [pyp5js](https://berinhard.github.io/pyp5js/) as a web-native graphing engine.\n",
+ "\n",
+ "The possibilities are endless and I can foresee spending way too much time on this. In this blog post, I will lay out the ideas behind this approach."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "ce3bd52d4200405b8184949d70c08cd0",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "# Playing with L-systems in Python\n",
+ "\n",
+ "There are different kinds of L-systems, with increasing complexity. We will start with the simplest: Lindenmayer's original L-system for modelling the growth of algae (We will jump right in, please read the [article on Wikipedia](https://en.wikipedia.org/wiki/L-system) if you need more context).\n",
+ "\n",
+ "## D0L: deterministic context-free L-system\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "cell_id": "4f89aef0f75d4aa3808305b92a4925d3",
+ "deepnote_cell_type": "code",
+ "deepnote_to_be_reexecuted": false,
+ "execution_millis": 21,
+ "execution_start": 1619612317163,
+ "source_hash": "8b352d4c",
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0: A\n",
+ "1: AB\n",
+ "2: ABA\n",
+ "3: ABAAB\n",
+ "4: ABAABABA\n",
+ "5: ABAABABAABAAB\n",
+ "6: ABAABABAABAABABAABABA\n",
+ "7: ABAABABAABAABABAABABAABAABABAABAAB\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# define L-system\n",
+ "AXIOM = 'A'\n",
+ "RULES = {'A': 'AB',\n",
+ " 'B': 'A'}\n",
+ "\n",
+ "\n",
+ "# initialize \n",
+ "productions = [AXIOM]\n",
+ "iterations = 7\n",
+ "\n",
+ "\n",
+ "def generate_d0l(axiom, productions, iterations):\n",
+ " def rewrite_l(word):\n",
+ " productions.append(''.join([RULES.get(c) or c for c in word]))\n",
+ " return productions[-1]\n",
+ "\n",
+ "\n",
+ " if iterations == 0:\n",
+ " return axiom\n",
+ " else:\n",
+ " return rewrite_l(generate_d0l(axiom, productions, iterations - 1))\n",
+ "\n",
+ "\n",
+ "# main\n",
+ "generate_d0l(AXIOM, productions, iterations)\n",
+ "print(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "0abb04548758427aa75800c3d3fb8ae3",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "I actually found the recursive Python implementation on this [introductory website on recursion](https://understanding-recursion.readthedocs.io/en/latest/16%20L-System%20Solution.html). While I still struggle to apply recursion, I find it satisfying to solve coding problems this way. And even with just these twenty lines of code, we have already stumbled on the [Fibonacci numbers](https://en.wikipedia.org/wiki/Fibonacci_number)! Have a look at the length of each successive sequence:\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "cell_id": "7c9e0ab688d543ddb427e0706d09d8c1",
+ "deepnote_cell_type": "code",
+ "deepnote_to_be_reexecuted": false,
+ "execution_millis": 135,
+ "execution_start": 1619612317215,
+ "is_code_hidden": true,
+ "source_hash": "8264db4e",
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[1, 2, 3, 5, 8, 13, 21, 34]\n"
+ ]
+ }
+ ],
+ "source": [
+ "print([len(word) for word in productions])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "2c2bc972bb9c4fcba319367e675ad756",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "Awesome as the nature of code may be, we are still a long way off from actually generating a tree. For that, we need branching rules. To do so, basic L-systems also allow constants, which are left untouched by the production rules. It is common to add constants `+` and `-` to denote rotations when branching, and `[`,`]` for handling the locations of the branching points. For a fractal plant, the code is as follows:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "cell_id": "0edc13f7a3a94a8f8c6d39e03e99b6dd",
+ "deepnote_cell_type": "code",
+ "deepnote_to_be_reexecuted": false,
+ "execution_millis": 134,
+ "execution_start": 1619612317216,
+ "source_hash": "b4945e20",
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0: X\n",
+ "1: F+[[X]-X]-F[-FX]+X\n",
+ "2: FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X\n",
+ "3: FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X\n",
+ "4: FFFFFFFF+[[FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFFFFFF[-FFFFFFFFFFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X\n",
+ "5: FFFFFFFFFFFFFFFF+[[FFFFFFFF+[[FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFFFFFF[-FFFFFFFFFFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFFFFFF+[[FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFFFFFF[-FFFFFFFFFFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFFFFFFFFFFFFFF[-FFFFFFFFFFFFFFFFFFFFFFFF+[[FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFFFFFF[-FFFFFFFFFFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FFFFFFFF+[[FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-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+ "6: 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+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "AXIOM = \"X\"\n",
+ "RULES = {\"X\": \"F+[[X]-X]-F[-FX]+X\",\n",
+ " \"F\": \"FF\"}\n",
+ "productions = [AXIOM]\n",
+ "generate_d0l(AXIOM, productions, iterations)\n",
+ "print(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "aa7ef8890e03437da0f5ea9bb687cb59",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "It is amazing to see how complexity increases by adding slightly longer rules. To actually draw something, we translate the letters as follows:\n",
+ "* \"F\" means \"draw forward\"\n",
+ "* \"-\" means \"turn right\", using a predefined value e.g. 30°\n",
+ "* \"+\" means \"turn left 30°\"\n",
+ "* \"X\" does not correspond to any drawing action and is used to control the evolution of the curve.\n",
+ "\n",
+ "The square bracket \"\\[\" corresponds to saving the current values for position and angle, which are restored when the corresponding \"]\" is executed, which effectively is a [LIFO stack](https://en.wikipedia.org/wiki/Stack_(abstract_data_type)). We will go into the details of how to draw later."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "cedfb378ff2b437c947fd884ee69bed5",
+ "deepnote_cell_type": "markdown",
+ "deepnote_to_be_reexecuted": false,
+ "execution_millis": 35,
+ "execution_start": 1619388009090,
+ "source_hash": "fdd41db5",
+ "tags": []
+ },
+ "source": [
+ "## Adding stochastic rules\n",
+ "\n",
+ "D0L systems are completely deterministic, that is, each starting axiom yields the same result. Using this to draw a forest would result in a boring scene: all trees would be identical. To mimic mutations in nature, stochastic L-systems allow the same letter to have for different production rules with a given probability. For example, if we want three different production rules for F with equal probability\n",
+ "\n",
+ "```\n",
+ "p1: F(0.33) → F[+F]F[−F]F\n",
+ "p2: F(0.33) → F[+F]F\n",
+ "p3: F(0.34) → F[−F]F\n",
+ "```\n",
+ "\n",
+ "the Python implementation could look something like this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "cell_id": "4e3895f0f15b431a9489742b3f7cd84f",
+ "deepnote_cell_type": "code",
+ "deepnote_to_be_reexecuted": false,
+ "execution_millis": 10,
+ "execution_start": 1619612508337,
+ "source_hash": "77e3defc",
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0: F\n",
+ "1: F[−F]F\n",
+ "2: F[−F]F[−F[−F]F]F[−F]F\n",
+ "3: F[−F]F[−F[−F]F]F[−F]F[−F[−F]F[−F[+F]F]F[+F]F[−F]F]F[+F]F[−F[+F]F[−F]F]F[+F]F[−F]F\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "from numpy.random import default_rng\n",
+ "\n",
+ "AXIOM = \"F\"\n",
+ "RULES = {\"F\": [\"F[+F]F[−F]F\", \"F[+F]F\", \"F[−F]F\"]}\n",
+ "productions = [AXIOM]\n",
+ "iterations = 3\n",
+ "\n",
+ "\n",
+ "rng = default_rng()\n",
+ "def generate_stochastic(axiom, productions, iterations):\n",
+ " def get_stochastic_rule(letter):\n",
+ " if letter not in RULES.keys():\n",
+ " return letter\n",
+ " else:\n",
+ " return RULES.get(letter)[rng.choice(3,1)[0]]\n",
+ "\n",
+ "\n",
+ " def rewrite_l(word):\n",
+ " productions.append(''.join([get_stochastic_rule(c) for c in word]))\n",
+ " return productions[-1]\n",
+ "\n",
+ "\n",
+ " if iterations == 0:\n",
+ " return axiom\n",
+ " else:\n",
+ " return rewrite_l(generate_stochastic(axiom, productions, iterations - 1))\n",
+ "\n",
+ "\n",
+ "generate_stochastic(AXIOM, productions, iterations)\n",
+ "print(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "ed6a867aa5884874b555f482c88a9e5f",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "Here's another run with a different result:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "cell_id": "ec7650359b644649a843d7a30e0ce467",
+ "deepnote_cell_type": "code",
+ "deepnote_to_be_reexecuted": false,
+ "execution_millis": 0,
+ "execution_start": 1619612520082,
+ "is_code_hidden": true,
+ "source_hash": "32960fdd",
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0: F\n",
+ "1: F[+F]F[−F]F\n",
+ "2: F[+F]F[−F]F[+F[+F]F]F[−F]F[−F[+F]F[−F]F]F[+F]F[−F]F\n",
+ "3: F[−F]F[+F[+F]F]F[+F]F[−F[+F]F]F[+F]F[−F]F[+F[−F]F[+F[+F]F]F[−F]F]F[+F]F[−F[+F]F[−F]F]F[+F]F[−F]F[−F[−F]F[+F[−F]F]F[−F]F[−F[+F]F]F[+F]F[−F]F]F[+F]F[−F]F[+F[+F]F[−F]F]F[−F]F[−F[+F]F[−F]F]F[+F]F[−F]F\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# show that a new run generates different result\n",
+ "productions = [AXIOM]\n",
+ "generate_stochastic(AXIOM, productions, iterations)\n",
+ "print(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "4d37ba2098994f79a57b03abb2e8fb71",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "## Adding parameters\n",
+ "\n",
+ "In a parametric L-system, letters are allowed to have parameters, which correspond with formal parameters used in the specification of L-system productions. This can be used to model _Anabaena catenula_ (taken from [Hanan's dissertation](http://algorithmicbotany.org/papers/hanan.dis1992.html)):"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "cell_id": "ffbb155396f541bea91cdddafa44a742",
+ "deepnote_cell_type": "code",
+ "deepnote_to_be_reexecuted": false,
+ "execution_millis": 71,
+ "execution_start": 1619612317279,
+ "source_hash": "ddba2700",
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0: [F(s=1, t=2, o=1)]\n",
+ "1: [F(s=2, t=1, o=1)]\n",
+ "2: [F(s=2, t=1, o=-1), F(s=1, t=2, o=1)]\n",
+ "3: [F(s=1, t=2, o=-1), F(s=2, t=1, o=1), F(s=2, t=1, o=1)]\n",
+ "4: [F(s=2, t=1, o=-1), F(s=2, t=1, o=-1), F(s=1, t=2, o=1), F(s=2, t=1, o=-1), F(s=1, t=2, o=1)]\n",
+ "5: [F(s=1, t=2, o=-1), F(s=2, t=1, o=1), F(s=1, t=2, o=-1), F(s=2, t=1, o=1), F(s=2, t=1, o=1), F(s=1, t=2, o=-1), F(s=2, t=1, o=1), F(s=2, t=1, o=1)]\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "from collections import namedtuple\n",
+ "\n",
+ "\n",
+ "# parameters\n",
+ "F = namedtuple('F', ['s', 't', 'o']) # parameterized cell\n",
+ "s = {2: \"AS\", 1: \"BS\"} # cell size\n",
+ "t = {1: \"A\", 2: \"B\"} # cell type\n",
+ "o = {1: \"right\", -1: \"left\"} # cell orientation\n",
+ "\n",
+ "AXIOM = [F(1, 2, 1)]\n",
+ "RULES = {F(2,1,1): [F(2,1,-1), F(1,2,1)],\n",
+ " F(2,1,-1): [F(1,2,-1), F(2,1,1)],\n",
+ " F(1,2,1): [F(2,1,1)],\n",
+ " F(1,2,-1): [F(2,1,-1)],\n",
+ " }\n",
+ "productions = [AXIOM]\n",
+ "iterations = 5\n",
+ "\n",
+ "\n",
+ "def unnest(list_, unnested_=None):\n",
+ " \"\"\"Utility function to unnest arbitrarily deep list of lists\n",
+ " \"\"\"\n",
+ " if unnested_ is None:\n",
+ " unnested_ = []\n",
+ " for x in list_:\n",
+ " if not isinstance(x, list):\n",
+ " unnested_.append(x)\n",
+ " if isinstance(x, list):\n",
+ " unnest(x, unnested_)\n",
+ " return unnested_\n",
+ "\n",
+ "\n",
+ "def generate_parametric(axiom, productions, iterations):\n",
+ " def rewrite_l(word):\n",
+ " productions.append(unnest([RULES.get(c) or c for c in unnest(word)]))\n",
+ " return productions[-1]\n",
+ "\n",
+ "\n",
+ " if iterations == 0:\n",
+ " return [axiom]\n",
+ " else:\n",
+ " return rewrite_l(generate_parametric(axiom, productions, iterations - 1))\n",
+ "\n",
+ "\n",
+ "generate_parametric(AXIOM, productions, iterations)\n",
+ "print(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "c81bb3c6722640deb2d8b5e2a7a35fdb",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "\n",
+ "While the _Anabaena_ example above only makes simple comparisons, parametric L-systems can use any expression using the parameters in combination with the arithmetic operators +, −, ∗, /; the exponentiation operator ∧, the relational operators <, >, =; the logical operators !, &, | (not, and, or) etc. For example, we could define a parameter `time` which increases with every iteration. This could be used to thicken the width of a branch of a tree.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "3153eb8d46394822906ac6430be06f3c",
+ "deepnote_cell_type": "markdown",
+ "deepnote_to_be_reexecuted": false,
+ "execution_millis": 7,
+ "execution_start": 1619387455407,
+ "source_hash": "616536f3",
+ "tags": []
+ },
+ "source": [
+ "# Using pyp5js for Pythonic drawing on the web\n",
+ "\n",
+ "When Lindenmayer devised the L-system, [Logo](https://en.wikipedia.org/wiki/Logo_(programming_language)) was one of the few programming langauges available. It included [turtle graphics](https://en.wikipedia.org/wiki/Turtle_graphics) and thus the basis of algorithmic art was born by translating the alphabet of an L-system to turtle commands. The examples from the Nature of Code have in fact [implemented this in Processing](https://github.com/nature-of-code/noc-examples-processing/blob/master/chp08_fractals/NOC_8_09_LSystem/Turtle.pde). But rather than constrain yourself to the desktop, more mileage can be had by using [p5js](https://p5js.org) which is \"... an interpretation of Processing for today's web\". To demonstrate, take the following example:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "cell_id": "339bc90f77ba4f03ae639db0ba417ad8",
+ "deepnote_cell_type": "code",
+ "deepnote_to_be_reexecuted": false,
+ "execution_millis": 73,
+ "execution_start": 1619612317283,
+ "source_hash": "cbe4ac7d",
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0: G\n",
+ "1: F-[[G]+G]+F[+FG]-G\n",
+ "2: FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G\n",
+ "3: FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G\n",
+ "4: FFFFFFFF-[[FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFFFFFF[+FFFFFFFFFFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G\n",
+ "5: FFFFFFFFFFFFFFFF-[[FFFFFFFF-[[FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFFFFFF[+FFFFFFFFFFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFFFFFF-[[FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFFFFFF[+FFFFFFFFFFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFFFFFFFFFFFFFF[+FFFFFFFFFFFFFFFFFFFFFFFF-[[FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFFFFFF[+FFFFFFFFFFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FFFFFFFF-[[FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFFFFFF[+FFFFFFFFFFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "AXIOM = 'G'\n",
+ "RULES = {\n",
+ " 'F': 'FF',\n",
+ " 'G': 'F-[[G]+G]+F[+FG]-G'\n",
+ "}\n",
+ "productions = [AXIOM]\n",
+ "generate_d0l(AXIOM, productions, iterations=5)\n",
+ "print(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "0ca8b0c2a4124b53bed66534c630dcb6",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "Summer Rizo has already implemented L-systems in p5js, available on [thefractal.zone](https://thefractal.zone/). Copying the axiom and rules, and setting the branching angle $\\theta$ to 30°, yields the drawing below. Note that the code only shows 5 iterations, while the drawing is based on more iterations (I have put the slider on maximum). When using recursion in Python you may quickly hit a limit: as I tried to execute `iterations=10` on a standard VM, Deepnote threw an error `IOPub data rate exceeded`. Yet another challenge to read-up and use [tail-call optimization in Python](https://sagnibak.github.io/blog/python-is-haskell-tail-recursion/)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "zsh:1: unknown file attribute: i\r\n"
+ ]
+ }
+ ],
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "ab0730498f754a9497120d0e9a5a78a4",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "Having covered the algorithmic and technical components, we can now start bringing it all together. There are still quite a few things to experiment with in order to produce realistic sketches, such as adding noise to draw 'sketchy' lines, adding thickness to branches, adding shadows with brightness off-sets and composing a scene with overlaying trees. As a Pythonista I was happy to find [pyp5js](https://berinhard.github.io/pyp5js/), which allows you to re-use the ideas of Processing in Python, and transcoding it to p5.js using Transcrypt. It covers all the methods from p5.js and gives us enough drawing tools to play with. But that's for another post. For now, I will leave you with a [generative creation from Anders Hoff](https://inconvergent.net/generative/) which may inspire you to start creating generative art in Python, too.\n",
+ "\n",
+ ""
+ ]
+ }
+ ],
+ "metadata": {
+ "deepnote": {
+ "is_reactive": false
+ },
+ "deepnote_execution_queue": [],
+ "deepnote_notebook_id": "94e2a17bd9324e6db3fff66e4a015929",
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.13"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
diff --git a/src/blog/posts/eerlijke-algoritmen.qmd b/src/blog/posts/eerlijke-algoritmen.qmd
index b67d539..1bb5ae4 100644
--- a/src/blog/posts/eerlijke-algoritmen.qmd
+++ b/src/blog/posts/eerlijke-algoritmen.qmd
@@ -8,7 +8,7 @@ date-format: short
image: /images/alexander-grey-TZZwC_xsClY-unsplash.jpg
html:
code-fold: true
-categories: [nederlands, Responsible AI]
+categories: [nederlands, responsible ai]
---
Het gebruik van algoritmen voor toezicht door de overheid blijft een heikel punt. Bij het verschijnen van het vierde en vijfde rapport over de Fraudesignaleringsvoorziening (FSV) bij de Belastingdienst.[^1] liet de politiek geen kans onbenut om in krachtige termen haar ongenoegen te uiten: ‘schandalig’, ‘racistisch’, ‘woest makend’ en ‘oneerlijk’. In de Tweede Kamer werd met ruime meerderheid een motie aangenomen[^2] om impact assessments verplicht te stellen ter voorkoming van misbruik van algoritmen. Maar om tot eerlijke algoritmen te komen, is meer nodig.
diff --git a/src/blog/posts/lartpy.ipynb b/src/blog/posts/lartpy.ipynb
index efe5d24..d36fc37 100644
--- a/src/blog/posts/lartpy.ipynb
+++ b/src/blog/posts/lartpy.ipynb
@@ -1 +1,562 @@
-{"cells":[{"cell_type":"markdown","metadata":{"cell_id":"74580f134ddc410bafde8c5caffa5364","deepnote_cell_type":"markdown","tags":[]},"source":["# L'art pour l'art: creating generative art with L-systems in Python\n","\n","\n","\n","[Creative coding](https://en.wikipedia.org/wiki/Creative_coding) is fun if you know a thing or two about programming. And if, like me, you are an utter noob when it comes to brushes and pencils, then it is even more enticing as a means to express yourself and create something just for the sake of it. It doesn't have to be functional, but you do get to hone your hacking skills and set challenges for yourself along the way.\n","\n","A fellow data scientist who is into [\"Art & AI\"](https://www.basbloemberg.nl/) recently pointed me to the field of [generative art](https://aiartists.org/generative-art-design). I have always been facinated by [emergence](https://en.wikipedia.org/wiki/Emergence) and even more so when I came across the picture above. It is featured in [this blog](https://g-e-n-a-r-t.com/en/post.php?p=10) on how to draw a pencil-sketch-like forest with Processing. One thing led to another: I had a go at [Processing in Python mode](https://py.processing.org/tutorials/command-line/), dabbled with [matplotlib for animations](http://louistiao.me/posts/notebooks/embedding-matplotlib-animations-in-jupyter-as-interactive-javascript-widgets/) and read Schiffman's [the Nature of Code](https://natureofcode.com/book/).\n","\n","_\"Would it be possible to create a Python project that can generate those pencil-like drawings with random forests, with different types of trees?\"_, I thought (pun intended). Of course, someone already thought of that and it even has a name: __algorithmic botany__. Przemyslaw Prusinkiewicz and Aristid Lindenmayer wrote the seminal book on the subject in 1990, [The Algorithmic Beauty of Plants](http://algorithmicbotany.org/papers/#abop). Lindenmayer invented [L-systems](https://en.wikipedia.org/wiki/L-system) already back in 1968. Today, household computers have enough resources to handle large-ish parallel writing systems and you could start modelling the growth of any plant using a framework like [L-Py](https://lpy.readthedocs.io/en/latest/).\n","\n","Although a lot has been written on the subject and there are quite a few open source libraries, they weren't quite what I have in mind. Instead, the idea of creating generative art in Python emerged using the following components:\n","\n","1. A lightweight implementation of L-systems that also supports stochastic and parametric production rules;\n","2. Integration with [p5js](https://p5js.org) via [pyp5js](https://berinhard.github.io/pyp5js/) as a web-native graphing engine.\n","\n","The possibilities are endless and I can foresee spending way too much time on this. In this blog post, I will lay out the ideas behind this approach."]},{"cell_type":"markdown","metadata":{"cell_id":"ce3bd52d4200405b8184949d70c08cd0","deepnote_cell_type":"markdown","tags":[]},"source":["# Playing with L-systems in Python\n","\n","There are different kinds of L-systems, with increasing complexity. We will start with the simplest: Lindenmayer's original L-system for modelling the growth of algae (We will jump right in, please read the [article on Wikipedia](https://en.wikipedia.org/wiki/L-system) if you need more context).\n","\n","## D0L: deterministic context-free L-system\n"]},{"cell_type":"code","execution_count":null,"metadata":{"cell_id":"4f89aef0f75d4aa3808305b92a4925d3","deepnote_cell_type":"code","deepnote_to_be_reexecuted":false,"execution_millis":21,"execution_start":1619612317163,"source_hash":"8b352d4c","tags":[]},"outputs":[{"name":"stdout","output_type":"stream","text":["0: A\n","1: AB\n","2: ABA\n","3: ABAAB\n","4: ABAABABA\n","5: ABAABABAABAAB\n","6: ABAABABAABAABABAABABA\n","7: ABAABABAABAABABAABABAABAABABAABAAB\n","\n"]}],"source":["# define L-system\n","AXIOM = 'A'\n","RULES = {'A': 'AB',\n"," 'B': 'A'}\n","\n","\n","# initialize \n","productions = [AXIOM]\n","iterations = 7\n","\n","\n","def generate_d0l(axiom, productions, iterations):\n"," def rewrite_l(word):\n"," productions.append(''.join([RULES.get(c) or c for c in word]))\n"," return productions[-1]\n","\n","\n"," if iterations == 0:\n"," return axiom\n"," else:\n"," return rewrite_l(generate_d0l(axiom, productions, iterations - 1))\n","\n","\n","# main\n","generate_d0l(AXIOM, productions, iterations)\n","print(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))"]},{"cell_type":"markdown","metadata":{"cell_id":"0abb04548758427aa75800c3d3fb8ae3","deepnote_cell_type":"markdown","tags":[]},"source":["I actually found the recursive Python implementation on this [introductory website on recursion](https://understanding-recursion.readthedocs.io/en/latest/16%20L-System%20Solution.html). While I still struggle to apply recursion, I find it satisfying to solve coding problems this way. And even with just these twenty lines of code, we have already stumbled on the [Fibonacci numbers](https://en.wikipedia.org/wiki/Fibonacci_number)! Have a look at the length of each successive sequence:\n"]},{"cell_type":"code","execution_count":null,"metadata":{"cell_id":"7c9e0ab688d543ddb427e0706d09d8c1","deepnote_cell_type":"code","deepnote_to_be_reexecuted":false,"execution_millis":135,"execution_start":1619612317215,"is_code_hidden":true,"source_hash":"8264db4e","tags":[]},"outputs":[{"name":"stdout","output_type":"stream","text":["[1, 2, 3, 5, 8, 13, 21, 34]\n"]}],"source":["print([len(word) for word in productions])"]},{"cell_type":"markdown","metadata":{"cell_id":"2c2bc972bb9c4fcba319367e675ad756","deepnote_cell_type":"markdown","tags":[]},"source":["Awesome as the nature of code may be, we are still a long way off from actually generating a tree. For that, we need branching rules. To do so, basic L-systems also allow constants, which are left untouched by the production rules. It is common to add constants `+` and `-` to denote rotations when branching, and `[`,`]` for handling the locations of the branching points. For a fractal plant, the code is as follows:"]},{"cell_type":"code","execution_count":null,"metadata":{"cell_id":"0edc13f7a3a94a8f8c6d39e03e99b6dd","deepnote_cell_type":"code","deepnote_to_be_reexecuted":false,"execution_millis":134,"execution_start":1619612317216,"source_hash":"b4945e20","tags":[]},"outputs":[{"name":"stdout","output_type":"stream","text":["0: X\n","1: F+[[X]-X]-F[-FX]+X\n","2: FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X\n","3: FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X\n","4: 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= \"X\"\n","RULES = {\"X\": \"F+[[X]-X]-F[-FX]+X\",\n"," \"F\": \"FF\"}\n","productions = [AXIOM]\n","generate_d0l(AXIOM, productions, iterations)\n","print(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))"]},{"cell_type":"markdown","metadata":{"cell_id":"aa7ef8890e03437da0f5ea9bb687cb59","deepnote_cell_type":"markdown","tags":[]},"source":["It is amazing to see how complexity increases by adding slightly longer rules. To actually draw something, we translate the letters as follows:\n","* \"F\" means \"draw forward\"\n","* \"-\" means \"turn right\", using a predefined value e.g. 30°\n","* \"+\" means \"turn left 30°\"\n","* \"X\" does not correspond to any drawing action and is used to control the evolution of the curve.\n","\n","The square bracket \"\\[\" corresponds to saving the current values for position and angle, which are restored when the corresponding \"]\" is executed, which effectively is a [LIFO stack](https://en.wikipedia.org/wiki/Stack_(abstract_data_type)). We will go into the details of how to draw later."]},{"cell_type":"markdown","metadata":{"cell_id":"cedfb378ff2b437c947fd884ee69bed5","deepnote_cell_type":"markdown","deepnote_to_be_reexecuted":false,"execution_millis":35,"execution_start":1619388009090,"source_hash":"fdd41db5","tags":[]},"source":["## Adding stochastic rules\n","\n","D0L systems are completely deterministic, that is, each starting axiom yields the same result. Using this to draw a forest would result in a boring scene: all trees would be identical. To mimic mutations in nature, stochastic L-systems allow the same letter to have for different production rules with a given probability. For example, if we want three different production rules for F with equal probability\n","\n","```\n","p1: F(0.33) → F[+F]F[−F]F\n","p2: F(0.33) → F[+F]F\n","p3: F(0.34) → F[−F]F\n","```\n","\n","the Python implementation could look something like this:"]},{"cell_type":"code","execution_count":null,"metadata":{"cell_id":"4e3895f0f15b431a9489742b3f7cd84f","deepnote_cell_type":"code","deepnote_to_be_reexecuted":false,"execution_millis":10,"execution_start":1619612508337,"source_hash":"77e3defc","tags":[]},"outputs":[{"name":"stdout","output_type":"stream","text":["0: F\n","1: F[−F]F\n","2: F[−F]F[−F[−F]F]F[−F]F\n","3: F[−F]F[−F[−F]F]F[−F]F[−F[−F]F[−F[+F]F]F[+F]F[−F]F]F[+F]F[−F[+F]F[−F]F]F[+F]F[−F]F\n","\n"]}],"source":["from numpy.random import default_rng\n","\n","AXIOM = \"F\"\n","RULES = {\"F\": [\"F[+F]F[−F]F\", \"F[+F]F\", \"F[−F]F\"]}\n","productions = [AXIOM]\n","iterations = 3\n","\n","\n","rng = default_rng()\n","def generate_stochastic(axiom, productions, iterations):\n"," def get_stochastic_rule(letter):\n"," if letter not in RULES.keys():\n"," return letter\n"," else:\n"," return RULES.get(letter)[rng.choice(3,1)[0]]\n","\n","\n"," def rewrite_l(word):\n"," productions.append(''.join([get_stochastic_rule(c) for c in word]))\n"," return productions[-1]\n","\n","\n"," if iterations == 0:\n"," return axiom\n"," else:\n"," return rewrite_l(generate_stochastic(axiom, productions, iterations - 1))\n","\n","\n","generate_stochastic(AXIOM, productions, iterations)\n","print(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))"]},{"cell_type":"markdown","metadata":{"cell_id":"ed6a867aa5884874b555f482c88a9e5f","deepnote_cell_type":"markdown","tags":[]},"source":["Here's another run with a different result:"]},{"cell_type":"code","execution_count":null,"metadata":{"cell_id":"ec7650359b644649a843d7a30e0ce467","deepnote_cell_type":"code","deepnote_to_be_reexecuted":false,"execution_millis":0,"execution_start":1619612520082,"is_code_hidden":true,"source_hash":"32960fdd","tags":[]},"outputs":[{"name":"stdout","output_type":"stream","text":["0: F\n","1: F[+F]F[−F]F\n","2: F[+F]F[−F]F[+F[+F]F]F[−F]F[−F[+F]F[−F]F]F[+F]F[−F]F\n","3: F[−F]F[+F[+F]F]F[+F]F[−F[+F]F]F[+F]F[−F]F[+F[−F]F[+F[+F]F]F[−F]F]F[+F]F[−F[+F]F[−F]F]F[+F]F[−F]F[−F[−F]F[+F[−F]F]F[−F]F[−F[+F]F]F[+F]F[−F]F]F[+F]F[−F]F[+F[+F]F[−F]F]F[−F]F[−F[+F]F[−F]F]F[+F]F[−F]F\n","\n"]}],"source":["# show that a new run generates different result\n","productions = [AXIOM]\n","generate_stochastic(AXIOM, productions, iterations)\n","print(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))"]},{"cell_type":"markdown","metadata":{"cell_id":"4d37ba2098994f79a57b03abb2e8fb71","deepnote_cell_type":"markdown","tags":[]},"source":["## Adding parameters\n","\n","In a parametric L-system, letters are allowed to have parameters, which correspond with formal parameters used in the specification of L-system productions. This can be used to model _Anabaena catenula_ (taken from [Hanan's dissertation](http://algorithmicbotany.org/papers/hanan.dis1992.html)):"]},{"cell_type":"code","execution_count":null,"metadata":{"cell_id":"ffbb155396f541bea91cdddafa44a742","deepnote_cell_type":"code","deepnote_to_be_reexecuted":false,"execution_millis":71,"execution_start":1619612317279,"source_hash":"ddba2700","tags":[]},"outputs":[{"name":"stdout","output_type":"stream","text":["0: [F(s=1, t=2, o=1)]\n","1: [F(s=2, t=1, o=1)]\n","2: [F(s=2, t=1, o=-1), F(s=1, t=2, o=1)]\n","3: [F(s=1, t=2, o=-1), F(s=2, t=1, o=1), F(s=2, t=1, o=1)]\n","4: [F(s=2, t=1, o=-1), F(s=2, t=1, o=-1), F(s=1, t=2, o=1), F(s=2, t=1, o=-1), F(s=1, t=2, o=1)]\n","5: [F(s=1, t=2, o=-1), F(s=2, t=1, o=1), F(s=1, t=2, o=-1), F(s=2, t=1, o=1), F(s=2, t=1, o=1), F(s=1, t=2, o=-1), F(s=2, t=1, o=1), F(s=2, t=1, o=1)]\n","\n"]}],"source":["from collections import namedtuple\n","\n","\n","# parameters\n","F = namedtuple('F', ['s', 't', 'o']) # parameterized cell\n","s = {2: \"AS\", 1: \"BS\"} # cell size\n","t = {1: \"A\", 2: \"B\"} # cell type\n","o = {1: \"right\", -1: \"left\"} # cell orientation\n","\n","AXIOM = [F(1, 2, 1)]\n","RULES = {F(2,1,1): [F(2,1,-1), F(1,2,1)],\n"," F(2,1,-1): [F(1,2,-1), F(2,1,1)],\n"," F(1,2,1): [F(2,1,1)],\n"," F(1,2,-1): [F(2,1,-1)],\n"," }\n","productions = [AXIOM]\n","iterations = 5\n","\n","\n","def unnest(list_, unnested_=None):\n"," \"\"\"Utility function to unnest arbitrarily deep list of lists\n"," \"\"\"\n"," if unnested_ is None:\n"," unnested_ = []\n"," for x in list_:\n"," if not isinstance(x, list):\n"," unnested_.append(x)\n"," if isinstance(x, list):\n"," unnest(x, unnested_)\n"," return unnested_\n","\n","\n","def generate_parametric(axiom, productions, iterations):\n"," def rewrite_l(word):\n"," productions.append(unnest([RULES.get(c) or c for c in unnest(word)]))\n"," return productions[-1]\n","\n","\n"," if iterations == 0:\n"," return [axiom]\n"," else:\n"," return rewrite_l(generate_parametric(axiom, productions, iterations - 1))\n","\n","\n","generate_parametric(AXIOM, productions, iterations)\n","print(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))"]},{"cell_type":"markdown","metadata":{"cell_id":"c81bb3c6722640deb2d8b5e2a7a35fdb","deepnote_cell_type":"markdown","tags":[]},"source":["\n","While the _Anabaena_ example above only makes simple comparisons, parametric L-systems can use any expression using the parameters in combination with the arithmetic operators +, −, ∗, /; the exponentiation operator ∧, the relational operators <, >, =; the logical operators !, &, | (not, and, or) etc. For example, we could define a parameter `time` which increases with every iteration. This could be used to thicken the width of a branch of a tree.\n"]},{"cell_type":"markdown","metadata":{"cell_id":"3153eb8d46394822906ac6430be06f3c","deepnote_cell_type":"markdown","deepnote_to_be_reexecuted":false,"execution_millis":7,"execution_start":1619387455407,"source_hash":"616536f3","tags":[]},"source":["# Using pyp5js for Pythonic drawing on the web\n","\n","When Lindenmayer devised the L-system, [Logo](https://en.wikipedia.org/wiki/Logo_(programming_language)) was one of the few programming langauges available. It included [turtle graphics](https://en.wikipedia.org/wiki/Turtle_graphics) and thus the basis of algorithmic art was born by translating the alphabet of an L-system to turtle commands. The examples from the Nature of Code have in fact [implemented this in Processing](https://github.com/nature-of-code/noc-examples-processing/blob/master/chp08_fractals/NOC_8_09_LSystem/Turtle.pde). But rather than constrain yourself to the desktop, more mileage can be had by using [p5js](https://p5js.org) which is \"... an interpretation of Processing for today's web\". To demonstrate, take the following example:"]},{"cell_type":"code","execution_count":null,"metadata":{"cell_id":"339bc90f77ba4f03ae639db0ba417ad8","deepnote_cell_type":"code","deepnote_to_be_reexecuted":false,"execution_millis":73,"execution_start":1619612317283,"source_hash":"cbe4ac7d","tags":[]},"outputs":[{"name":"stdout","output_type":"stream","text":["0: G\n","1: F-[[G]+G]+F[+FG]-G\n","2: FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G\n","3: FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G\n","4: 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= 'G'\n","RULES = {\n"," 'F': 'FF',\n"," 'G': 'F-[[G]+G]+F[+FG]-G'\n","}\n","productions = [AXIOM]\n","generate_d0l(AXIOM, productions, iterations=5)\n","print(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))"]},{"cell_type":"markdown","metadata":{"cell_id":"0ca8b0c2a4124b53bed66534c630dcb6","deepnote_cell_type":"markdown","tags":[]},"source":["Summer Rizo has already implemented L-systems in p5js, available on [thefractal.zone](https://thefractal.zone/). Copying the axiom and rules, and setting the branching angle $\\theta$ to 30°, yields the drawing below. Note that the code only shows 5 iterations, while the drawing is based on more iterations (I have put the slider on maximum). When using recursion in Python you may quickly hit a limit: as I tried to execute `iterations=10` on a standard VM, Deepnote threw an error `IOPub data rate exceeded`. Yet another challenge to read-up and use [tail-call optimization in Python](https://sagnibak.github.io/blog/python-is-haskell-tail-recursion/)."]},{"cell_type":"markdown","metadata":{"cell_id":"ab0730498f754a9497120d0e9a5a78a4","deepnote_cell_type":"markdown","tags":[]},"source":["Having covered the algorithmic and technical components, we can now start bringing it all together. There are still quite a few things to experiment with in order to produce realistic sketches, such as adding noise to draw 'sketchy' lines, adding thickness to branches, adding shadows with brightness off-sets and composing a scene with overlaying trees. As a Pythonista I was happy to find [pyp5js](https://berinhard.github.io/pyp5js/), which allows you to re-use the ideas of Processing in Python, and transcoding it to p5.js using Transcrypt. It covers all the methods from p5.js and gives us enough drawing tools to play with. But that's for another post. For now, I will leave you with a [generative creation from Anders Hoff](https://inconvergent.net/generative/) which may inspire you to start creating generative art in Python, too.\n","\n",""]},{"cell_type":"markdown","metadata":{"created_in_deepnote_cell":true,"deepnote_cell_type":"markdown"},"source":["\n"," \n","Created in Deepnote"]}],"metadata":{"deepnote":{"is_reactive":false},"deepnote_execution_queue":[],"deepnote_notebook_id":"94e2a17bd9324e6db3fff66e4a015929","language_info":{"name":"python"},"orig_nbformat":2},"nbformat":4,"nbformat_minor":0}
+{
+ "cells": [
+ {
+ "cell_type": "raw",
+ "metadata": {
+ "tags": []
+ },
+ "source": [
+ "---\n",
+ "title: Creating generative art with L-systems in Python\n",
+ "subtitle: Some experiments on the algorithmic beauty of plants\n",
+ "description: |\n",
+ " Would it be possible to create a Python project that can generate those pencil-like drawings with random forests, with different types of trees?\", I thought (pun intended). Of course, someone already thought of that and it even has a name: algorithmic botany.\n",
+ "date: 2021-04-26\n",
+ "date-format: short\n",
+ "image: /images/lartpy.jpg\n",
+ "categories: [english, visualization, generative art, coding]\n",
+ "---"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "74580f134ddc410bafde8c5caffa5364",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "\n",
+ "\n",
+ "[Creative coding](https://en.wikipedia.org/wiki/Creative_coding) is fun if you know a thing or two about programming. And if, like me, you are an utter noob when it comes to brushes and pencils, then it is even more enticing as a means to express yourself and create something just for the sake of it. It doesn't have to be functional, but you do get to hone your hacking skills and set challenges for yourself along the way.\n",
+ "\n",
+ "A fellow data scientist who is into [\"Art & AI\"](https://www.basbloemberg.nl/) recently pointed me to the field of [generative art](https://aiartists.org/generative-art-design). I have always been facinated by [emergence](https://en.wikipedia.org/wiki/Emergence) and even more so when I came across the picture above. It is featured in [this blog](https://g-e-n-a-r-t.com/en/post.php?p=10) on how to draw a pencil-sketch-like forest with Processing. One thing led to another: I had a go at [Processing in Python mode](https://py.processing.org/tutorials/command-line/), dabbled with [matplotlib for animations](http://louistiao.me/posts/notebooks/embedding-matplotlib-animations-in-jupyter-as-interactive-javascript-widgets/) and read Schiffman's [the Nature of Code](https://natureofcode.com/book/).\n",
+ "\n",
+ "_\"Would it be possible to create a Python project that can generate those pencil-like drawings with random forests, with different types of trees?\"_, I thought (pun intended). Of course, someone already thought of that and it even has a name: __algorithmic botany__. Przemyslaw Prusinkiewicz and Aristid Lindenmayer wrote the seminal book on the subject in 1990, [The Algorithmic Beauty of Plants](http://algorithmicbotany.org/papers/#abop). Lindenmayer invented [L-systems](https://en.wikipedia.org/wiki/L-system) already back in 1968. Today, household computers have enough resources to handle large-ish parallel writing systems and you could start modelling the growth of any plant using a framework like [L-Py](https://lpy.readthedocs.io/en/latest/).\n",
+ "\n",
+ "Although a lot has been written on the subject and there are quite a few open source libraries, they weren't quite what I have in mind. Instead, the idea of creating generative art in Python emerged using the following components:\n",
+ "\n",
+ "1. A lightweight implementation of L-systems that also supports stochastic and parametric production rules;\n",
+ "2. Integration with [p5js](https://p5js.org) via [pyp5js](https://berinhard.github.io/pyp5js/) as a web-native graphing engine.\n",
+ "\n",
+ "The possibilities are endless and I can foresee spending way too much time on this. In this blog post, I will lay out the ideas behind this approach."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "ce3bd52d4200405b8184949d70c08cd0",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "# Playing with L-systems in Python\n",
+ "\n",
+ "There are different kinds of L-systems, with increasing complexity. We will start with the simplest: Lindenmayer's original L-system for modelling the growth of algae (We will jump right in, please read the [article on Wikipedia](https://en.wikipedia.org/wiki/L-system) if you need more context).\n",
+ "\n",
+ "## D0L: deterministic context-free L-system\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "cell_id": "4f89aef0f75d4aa3808305b92a4925d3",
+ "deepnote_cell_type": "code",
+ "deepnote_to_be_reexecuted": false,
+ "execution_millis": 21,
+ "execution_start": 1619612317163,
+ "source_hash": "8b352d4c",
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0: A\n",
+ "1: AB\n",
+ "2: ABA\n",
+ "3: ABAAB\n",
+ "4: ABAABABA\n",
+ "5: ABAABABAABAAB\n",
+ "6: ABAABABAABAABABAABABA\n",
+ "7: ABAABABAABAABABAABABAABAABABAABAAB\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# define L-system\n",
+ "AXIOM = 'A'\n",
+ "RULES = {'A': 'AB',\n",
+ " 'B': 'A'}\n",
+ "\n",
+ "\n",
+ "# initialize \n",
+ "productions = [AXIOM]\n",
+ "iterations = 7\n",
+ "\n",
+ "\n",
+ "def generate_d0l(axiom, productions, iterations):\n",
+ " def rewrite_l(word):\n",
+ " productions.append(''.join([RULES.get(c) or c for c in word]))\n",
+ " return productions[-1]\n",
+ "\n",
+ "\n",
+ " if iterations == 0:\n",
+ " return axiom\n",
+ " else:\n",
+ " return rewrite_l(generate_d0l(axiom, productions, iterations - 1))\n",
+ "\n",
+ "\n",
+ "# main\n",
+ "generate_d0l(AXIOM, productions, iterations)\n",
+ "print(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "0abb04548758427aa75800c3d3fb8ae3",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "I actually found the recursive Python implementation on this [introductory website on recursion](https://understanding-recursion.readthedocs.io/en/latest/16%20L-System%20Solution.html). While I still struggle to apply recursion, I find it satisfying to solve coding problems this way. And even with just these twenty lines of code, we have already stumbled on the [Fibonacci numbers](https://en.wikipedia.org/wiki/Fibonacci_number)! Have a look at the length of each successive sequence:\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "cell_id": "7c9e0ab688d543ddb427e0706d09d8c1",
+ "deepnote_cell_type": "code",
+ "deepnote_to_be_reexecuted": false,
+ "execution_millis": 135,
+ "execution_start": 1619612317215,
+ "is_code_hidden": true,
+ "source_hash": "8264db4e",
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[1, 2, 3, 5, 8, 13, 21, 34]\n"
+ ]
+ }
+ ],
+ "source": [
+ "print([len(word) for word in productions])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "2c2bc972bb9c4fcba319367e675ad756",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "Awesome as the nature of code may be, we are still a long way off from actually generating a tree. For that, we need branching rules. To do so, basic L-systems also allow constants, which are left untouched by the production rules. It is common to add constants `+` and `-` to denote rotations when branching, and `[`,`]` for handling the locations of the branching points. For a fractal plant, the code is as follows:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "cell_id": "0edc13f7a3a94a8f8c6d39e03e99b6dd",
+ "deepnote_cell_type": "code",
+ "deepnote_to_be_reexecuted": false,
+ "execution_millis": 134,
+ "execution_start": 1619612317216,
+ "source_hash": "b4945e20",
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0: X\n",
+ "1: F+[[X]-X]-F[-FX]+X\n",
+ "2: FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X\n",
+ "3: FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X\n",
+ "4: FFFFFFFF+[[FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFFFFFF[-FFFFFFFFFFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X\n",
+ "5: FFFFFFFFFFFFFFFF+[[FFFFFFFF+[[FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFFFFFF[-FFFFFFFFFFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFFFFFF+[[FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFFFFFF[-FFFFFFFFFFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFFFFFFFFFFFFFF[-FFFFFFFFFFFFFFFFFFFFFFFF+[[FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFFFFFF[-FFFFFFFFFFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]+FFFFFFFF+[[FFFF+[[FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-X]-F[-FX]+X]-FFFF[-FFFFFF+[[F+[[X]-X]-F[-FX]+X]-F+[[X]-X]-F[-FX]+X]-FF[-FFF+[[X]-X]-F[-FX]+X]+F+[[X]-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+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "AXIOM = \"X\"\n",
+ "RULES = {\"X\": \"F+[[X]-X]-F[-FX]+X\",\n",
+ " \"F\": \"FF\"}\n",
+ "productions = [AXIOM]\n",
+ "generate_d0l(AXIOM, productions, iterations)\n",
+ "print(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "aa7ef8890e03437da0f5ea9bb687cb59",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "It is amazing to see how complexity increases by adding slightly longer rules. To actually draw something, we translate the letters as follows:\n",
+ "* \"F\" means \"draw forward\"\n",
+ "* \"-\" means \"turn right\", using a predefined value e.g. 30°\n",
+ "* \"+\" means \"turn left 30°\"\n",
+ "* \"X\" does not correspond to any drawing action and is used to control the evolution of the curve.\n",
+ "\n",
+ "The square bracket \"\\[\" corresponds to saving the current values for position and angle, which are restored when the corresponding \"]\" is executed, which effectively is a [LIFO stack](https://en.wikipedia.org/wiki/Stack_(abstract_data_type)). We will go into the details of how to draw later."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "cedfb378ff2b437c947fd884ee69bed5",
+ "deepnote_cell_type": "markdown",
+ "deepnote_to_be_reexecuted": false,
+ "execution_millis": 35,
+ "execution_start": 1619388009090,
+ "source_hash": "fdd41db5",
+ "tags": []
+ },
+ "source": [
+ "## Adding stochastic rules\n",
+ "\n",
+ "D0L systems are completely deterministic, that is, each starting axiom yields the same result. Using this to draw a forest would result in a boring scene: all trees would be identical. To mimic mutations in nature, stochastic L-systems allow the same letter to have for different production rules with a given probability. For example, if we want three different production rules for F with equal probability\n",
+ "\n",
+ "```\n",
+ "p1: F(0.33) → F[+F]F[−F]F\n",
+ "p2: F(0.33) → F[+F]F\n",
+ "p3: F(0.34) → F[−F]F\n",
+ "```\n",
+ "\n",
+ "the Python implementation could look something like this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "cell_id": "4e3895f0f15b431a9489742b3f7cd84f",
+ "deepnote_cell_type": "code",
+ "deepnote_to_be_reexecuted": false,
+ "execution_millis": 10,
+ "execution_start": 1619612508337,
+ "source_hash": "77e3defc",
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0: F\n",
+ "1: F[−F]F\n",
+ "2: F[−F]F[−F[−F]F]F[−F]F\n",
+ "3: F[−F]F[−F[−F]F]F[−F]F[−F[−F]F[−F[+F]F]F[+F]F[−F]F]F[+F]F[−F[+F]F[−F]F]F[+F]F[−F]F\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "from numpy.random import default_rng\n",
+ "\n",
+ "AXIOM = \"F\"\n",
+ "RULES = {\"F\": [\"F[+F]F[−F]F\", \"F[+F]F\", \"F[−F]F\"]}\n",
+ "productions = [AXIOM]\n",
+ "iterations = 3\n",
+ "\n",
+ "\n",
+ "rng = default_rng()\n",
+ "def generate_stochastic(axiom, productions, iterations):\n",
+ " def get_stochastic_rule(letter):\n",
+ " if letter not in RULES.keys():\n",
+ " return letter\n",
+ " else:\n",
+ " return RULES.get(letter)[rng.choice(3,1)[0]]\n",
+ "\n",
+ "\n",
+ " def rewrite_l(word):\n",
+ " productions.append(''.join([get_stochastic_rule(c) for c in word]))\n",
+ " return productions[-1]\n",
+ "\n",
+ "\n",
+ " if iterations == 0:\n",
+ " return axiom\n",
+ " else:\n",
+ " return rewrite_l(generate_stochastic(axiom, productions, iterations - 1))\n",
+ "\n",
+ "\n",
+ "generate_stochastic(AXIOM, productions, iterations)\n",
+ "print(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "ed6a867aa5884874b555f482c88a9e5f",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "Here's another run with a different result:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "cell_id": "ec7650359b644649a843d7a30e0ce467",
+ "deepnote_cell_type": "code",
+ "deepnote_to_be_reexecuted": false,
+ "execution_millis": 0,
+ "execution_start": 1619612520082,
+ "is_code_hidden": true,
+ "source_hash": "32960fdd",
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0: F\n",
+ "1: F[+F]F[−F]F\n",
+ "2: F[+F]F[−F]F[+F[+F]F]F[−F]F[−F[+F]F[−F]F]F[+F]F[−F]F\n",
+ "3: F[−F]F[+F[+F]F]F[+F]F[−F[+F]F]F[+F]F[−F]F[+F[−F]F[+F[+F]F]F[−F]F]F[+F]F[−F[+F]F[−F]F]F[+F]F[−F]F[−F[−F]F[+F[−F]F]F[−F]F[−F[+F]F]F[+F]F[−F]F]F[+F]F[−F]F[+F[+F]F[−F]F]F[−F]F[−F[+F]F[−F]F]F[+F]F[−F]F\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# show that a new run generates different result\n",
+ "productions = [AXIOM]\n",
+ "generate_stochastic(AXIOM, productions, iterations)\n",
+ "print(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "4d37ba2098994f79a57b03abb2e8fb71",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "## Adding parameters\n",
+ "\n",
+ "In a parametric L-system, letters are allowed to have parameters, which correspond with formal parameters used in the specification of L-system productions. This can be used to model _Anabaena catenula_ (taken from [Hanan's dissertation](http://algorithmicbotany.org/papers/hanan.dis1992.html)):"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "cell_id": "ffbb155396f541bea91cdddafa44a742",
+ "deepnote_cell_type": "code",
+ "deepnote_to_be_reexecuted": false,
+ "execution_millis": 71,
+ "execution_start": 1619612317279,
+ "source_hash": "ddba2700",
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0: [F(s=1, t=2, o=1)]\n",
+ "1: [F(s=2, t=1, o=1)]\n",
+ "2: [F(s=2, t=1, o=-1), F(s=1, t=2, o=1)]\n",
+ "3: [F(s=1, t=2, o=-1), F(s=2, t=1, o=1), F(s=2, t=1, o=1)]\n",
+ "4: [F(s=2, t=1, o=-1), F(s=2, t=1, o=-1), F(s=1, t=2, o=1), F(s=2, t=1, o=-1), F(s=1, t=2, o=1)]\n",
+ "5: [F(s=1, t=2, o=-1), F(s=2, t=1, o=1), F(s=1, t=2, o=-1), F(s=2, t=1, o=1), F(s=2, t=1, o=1), F(s=1, t=2, o=-1), F(s=2, t=1, o=1), F(s=2, t=1, o=1)]\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "from collections import namedtuple\n",
+ "\n",
+ "\n",
+ "# parameters\n",
+ "F = namedtuple('F', ['s', 't', 'o']) # parameterized cell\n",
+ "s = {2: \"AS\", 1: \"BS\"} # cell size\n",
+ "t = {1: \"A\", 2: \"B\"} # cell type\n",
+ "o = {1: \"right\", -1: \"left\"} # cell orientation\n",
+ "\n",
+ "AXIOM = [F(1, 2, 1)]\n",
+ "RULES = {F(2,1,1): [F(2,1,-1), F(1,2,1)],\n",
+ " F(2,1,-1): [F(1,2,-1), F(2,1,1)],\n",
+ " F(1,2,1): [F(2,1,1)],\n",
+ " F(1,2,-1): [F(2,1,-1)],\n",
+ " }\n",
+ "productions = [AXIOM]\n",
+ "iterations = 5\n",
+ "\n",
+ "\n",
+ "def unnest(list_, unnested_=None):\n",
+ " \"\"\"Utility function to unnest arbitrarily deep list of lists\n",
+ " \"\"\"\n",
+ " if unnested_ is None:\n",
+ " unnested_ = []\n",
+ " for x in list_:\n",
+ " if not isinstance(x, list):\n",
+ " unnested_.append(x)\n",
+ " if isinstance(x, list):\n",
+ " unnest(x, unnested_)\n",
+ " return unnested_\n",
+ "\n",
+ "\n",
+ "def generate_parametric(axiom, productions, iterations):\n",
+ " def rewrite_l(word):\n",
+ " productions.append(unnest([RULES.get(c) or c for c in unnest(word)]))\n",
+ " return productions[-1]\n",
+ "\n",
+ "\n",
+ " if iterations == 0:\n",
+ " return [axiom]\n",
+ " else:\n",
+ " return rewrite_l(generate_parametric(axiom, productions, iterations - 1))\n",
+ "\n",
+ "\n",
+ "generate_parametric(AXIOM, productions, iterations)\n",
+ "print(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "c81bb3c6722640deb2d8b5e2a7a35fdb",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "\n",
+ "While the _Anabaena_ example above only makes simple comparisons, parametric L-systems can use any expression using the parameters in combination with the arithmetic operators +, −, ∗, /; the exponentiation operator ∧, the relational operators <, >, =; the logical operators !, &, | (not, and, or) etc. For example, we could define a parameter `time` which increases with every iteration. This could be used to thicken the width of a branch of a tree.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "3153eb8d46394822906ac6430be06f3c",
+ "deepnote_cell_type": "markdown",
+ "deepnote_to_be_reexecuted": false,
+ "execution_millis": 7,
+ "execution_start": 1619387455407,
+ "source_hash": "616536f3",
+ "tags": []
+ },
+ "source": [
+ "# Using pyp5js for Pythonic drawing on the web\n",
+ "\n",
+ "When Lindenmayer devised the L-system, [Logo](https://en.wikipedia.org/wiki/Logo_(programming_language)) was one of the few programming langauges available. It included [turtle graphics](https://en.wikipedia.org/wiki/Turtle_graphics) and thus the basis of algorithmic art was born by translating the alphabet of an L-system to turtle commands. The examples from the Nature of Code have in fact [implemented this in Processing](https://github.com/nature-of-code/noc-examples-processing/blob/master/chp08_fractals/NOC_8_09_LSystem/Turtle.pde). But rather than constrain yourself to the desktop, more mileage can be had by using [p5js](https://p5js.org) which is \"... an interpretation of Processing for today's web\". To demonstrate, take the following example:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "cell_id": "339bc90f77ba4f03ae639db0ba417ad8",
+ "deepnote_cell_type": "code",
+ "deepnote_to_be_reexecuted": false,
+ "execution_millis": 73,
+ "execution_start": 1619612317283,
+ "source_hash": "cbe4ac7d",
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0: G\n",
+ "1: F-[[G]+G]+F[+FG]-G\n",
+ "2: FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G\n",
+ "3: FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G\n",
+ "4: FFFFFFFF-[[FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFFFFFF[+FFFFFFFFFFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FFFF-[[FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]+FFFF[+FFFFFF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G]-FF-[[F-[[G]+G]+F[+FG]-G]+F-[[G]+G]+F[+FG]-G]+FF[+FFF-[[G]+G]+F[+FG]-G]-F-[[G]+G]+F[+FG]-G\n",
+ "5: 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+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "AXIOM = 'G'\n",
+ "RULES = {\n",
+ " 'F': 'FF',\n",
+ " 'G': 'F-[[G]+G]+F[+FG]-G'\n",
+ "}\n",
+ "productions = [AXIOM]\n",
+ "generate_d0l(AXIOM, productions, iterations=5)\n",
+ "print(''.join([f\"{i}: {p}\\n\" for i,p in enumerate(productions)]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "0ca8b0c2a4124b53bed66534c630dcb6",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "Summer Rizo has already implemented L-systems in p5js, available on [thefractal.zone](https://thefractal.zone/). Copying the axiom and rules, and setting the branching angle $\\theta$ to 30°, yields the drawing below. Note that the code only shows 5 iterations, while the drawing is based on more iterations (I have put the slider on maximum). When using recursion in Python you may quickly hit a limit: as I tried to execute `iterations=10` on a standard VM, Deepnote threw an error `IOPub data rate exceeded`. Yet another challenge to read-up and use [tail-call optimization in Python](https://sagnibak.github.io/blog/python-is-haskell-tail-recursion/)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "cell_id": "ab0730498f754a9497120d0e9a5a78a4",
+ "deepnote_cell_type": "markdown",
+ "tags": []
+ },
+ "source": [
+ "Having covered the algorithmic and technical components, we can now start bringing it all together. There are still quite a few things to experiment with in order to produce realistic sketches, such as adding noise to draw 'sketchy' lines, adding thickness to branches, adding shadows with brightness off-sets and composing a scene with overlaying trees. As a Pythonista I was happy to find [pyp5js](https://berinhard.github.io/pyp5js/), which allows you to re-use the ideas of Processing in Python, and transcoding it to p5.js using Transcrypt. It covers all the methods from p5.js and gives us enough drawing tools to play with. But that's for another post. For now, I will leave you with a [generative creation from Anders Hoff](https://inconvergent.net/generative/) which may inspire you to start creating generative art in Python, too.\n",
+ "\n",
+ ""
+ ]
+ }
+ ],
+ "metadata": {
+ "deepnote": {
+ "is_reactive": false
+ },
+ "deepnote_execution_queue": [],
+ "deepnote_notebook_id": "94e2a17bd9324e6db3fff66e4a015929",
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.13"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
diff --git a/src/blog/posts/podcast-aitoday.qmd b/src/blog/posts/podcast-aitoday.qmd
new file mode 100644
index 0000000..7491a5c
--- /dev/null
+++ b/src/blog/posts/podcast-aitoday.qmd
@@ -0,0 +1,17 @@
+---
+title: Podcast bij AIToday
+subtitle: Geinterviewed door Joop Snijders en Niels Naglé
+description: Sinds tijden weer een _live_ gesprek!
+author: Daniel Kapitan
+date: 2022-07-05
+date-format: short
+image: /images/podcast-aitoday.jpg
+html:
+ code-fold: true
+categories: [nederlands, podcast, responsible ai]
+---
+
+
+```{=html}
+
+```
\ No newline at end of file
diff --git a/src/blog/posts/podcast-dataloog-datasolidariteit.qmd b/src/blog/posts/podcast-dataloog-datasolidariteit.qmd
new file mode 100644
index 0000000..26b3ba8
--- /dev/null
+++ b/src/blog/posts/podcast-dataloog-datasolidariteit.qmd
@@ -0,0 +1,17 @@
+---
+title: Podcast bij de Dataloog
+subtitle: Interview door Harm Bodewes en Jurjen Helmus
+description: Een heerlijk Socratisch gesprek over datasolidariteit
+author: Daniel Kapitan
+date: 2023-05-18
+date-format: short
+image: /images/podcast-de-dataloog.jpg
+html:
+ code-fold: true
+categories: [nederlands, podcast, data commons, data solidarity]
+---
+
+
+```{=html}
+
+```
\ No newline at end of file
diff --git a/src/temp b/src/temp
new file mode 100644
index 0000000..e69de29