Fractal Image Generators in SDL

GitHub Repository

https://github.com/daelsepara/sdl-fractals

Building (Unix/Linux)

cd repository/src
make

Dependencies: sdl2, sdl2-image

Usage

./Fractals.exe /PARAMS={parameters.json} /IMAGE={image.png} /PALETTE={palette.json} /BENCHMARK {other parameters}

Required parameters

/PARAMS={parameters.json} or /PARAMETERS={parameters.json}

Read parameters from {parameters.json} file.

See parameters/ for sample parameter files.

Optional parameters

/IMAGE={image.png}

Save fractal to {image.png}

/PALETTE={palette.json}

Use {palette.json} colormap. See palettes/ for some colormaps that can be used.

/BENCHMARK

Generate fractal in memory without rendering on the screen or saving image to {image.png}

Without /BENCHMARK and /IMAGE, the fractal is rendered on the screen.

Other parameters

/INVERTX

Inverts x-axis. Left to right goes from + to - values.

/INVERTY

Inverts y-axis. Top to bottom goes from - to + values.

/INVERT

Inverts color values.

/LOG

Use log-scale color mapping. Overrides color mapping in parameter file.

/NORMALIZED

Use normalized color mapping. Overrides color mapping in parameter file.

/MOD

Use moduluo-255 color mapping. Overrides color mapping in parameter file.

/HISTOGRAM

Use histogram color mapping. Overrides color mapping in parameter file.

/DEFAULT

Use default color mapping. Overrides color mapping in parameter file.

Examples

Mandelbrot Set

Parameters


Generator	z^exp + C
exponent	2
max iterations	255
escape value	4.0
parameter files	mandelbrot, mandelbrot2, mandelbrot3
palette	default
source(s)	Mandelbrot.hpp, Mandelbrot2.hpp, Mandelbrot3.hpp

Benchmarks

mandelbrot

Time (mean ± σ):     474.8 ms ±   7.7 ms    [User: 450.3 ms, System: 17.9 ms]
Range (min … max):   460.1 ms … 484.7 ms    10 runs

mandelbrot2

Time (mean ± σ):     382.1 ms ±   7.6 ms    [User: 359.3 ms, System: 17.4 ms]
Range (min … max):   375.8 ms … 401.5 ms    10 runs

mandelbrot3

Time (mean ± σ):     390.9 ms ±  11.6 ms    [User: 365.0 ms, System: 18.2 ms]
Range (min … max):   376.6 ms … 411.8 ms    10 runs

Newton

Parameters


Generator	z - (z^3 - 1)/(3z^2)
tolerance	1e-6
max iterations	255
parameter file	newton1
palette	default
source	Newton1.hpp

Time (mean ± σ):     868.1 ms ±   8.0 ms    [User: 822.9 ms, System: 35.2 ms]
Range (min … max):   855.1 ms … 882.9 ms    10 runs

Julia Sets

Common Parameters


Generator	z^exp + C
max iterations	255
escape value	4.0
source	Julia.hpp

Specific Parameters and Benchmarks


C	-0.4 + 0.6i
parameter file	julia1
palette	magma

Time (mean ± σ):     821.6 ms ±   8.3 ms    [User: 770.7 ms, System: 38.7 ms]
Range (min … max):   812.3 ms … 836.7 ms    10 runs


C	-0.8 + 0.156i
parameter file	julia2
palette	inferno

Time (mean ± σ):     936.7 ms ±  10.5 ms    [User: 881.0 ms, System: 39.5 ms]
Range (min … max):   925.1 ms … 959.9 ms    10 runs


C	0.285 + 0.01i
parameter file	julia3
palette	moreland

Time (mean ± σ):     732.1 ms ±  12.2 ms    [User: 678.0 ms, System: 38.8 ms]
Range (min … max):   718.5 ms … 755.8 ms    10 run


C	-0.7269 + 0.1889i
parameter file	julia4
palette	magma

Time (mean ± σ):      1.224 s ±  0.019 s    [User: 1.166 s, System: 0.041 s]
Range (min … max):    1.201 s …  1.263 s    10 runs


C	0.26294324588 - 0.0024215732998i
max iterations	320
normalized colormap	true
parameter file	julia5
palette	inverted jet

Time (mean ± σ):      3.495 s ±  0.027 s    [User: 3.428 s, System: 0.039 s]
Range (min … max):    3.454 s …  3.544 s    10 runs

Mandelbrot4

Parameters


Generator	z^exp + C
exponent	4
max iterations	255
escape value	4.0
parameter file	mandelbrot4
palette	default
source	Mandelbrot.hpp

Time (mean ± σ):      3.937 s ±  0.055 s    [User: 3.831 s, System: 0.056 s]
Range (min … max):    3.898 s …  4.063 s    10 runs

Burning Ship

Parameters


Generator	(Re(Zn) + iIm(Zn))^2 + C
inverted x	true
inverted y	true
normalized colormap	true
inside color	0
max iterations	100
escape value	4.0
parameter file	burningship
palette	hot
source	Mandelbrot.hpp

Time (mean ± σ):     559.9 ms ±   4.1 ms    [User: 518.1 ms, System: 33.7 ms]
Range (min … max):   552.8 ms … 567.2 ms    10 runs

Burning Ship (2)

Parameters


Generator	(Re(Zn) + iIm(Zn))^2 + C
inverted x	true
inverted y	true
log colormap	true
inside color	0
max iterations	100
escape value	4.0
parameter file	burningship2
palette	plasma
source	Mandelbrot.hpp

Time (mean ± σ):      1.469 s ±  0.289 s    [User: 0.840 s, System: 0.054 s]
Range (min … max):    1.248 s …  2.128 s    10 runs

Burning Ship (3)

Parameters


Generator	(Re(Zn) + iIm(Zn))^2 + C
inverted x	true
inverted y	true
log colormap	true
inside color	0
max iterations	100
escape value	4.0
parameter file	burningship3
palette	bluered
source	Mandelbrot.hpp

Time (mean ± σ):      1.469 s ±  0.289 s    [User: 0.840 s, System: 0.054 s]
Range (min … max):    1.248 s …  2.128 s    10 runs

Tricorn

Parameters


Generator	(z_x^2 + z_y^2) - i(2 * z_x * z_y) + C
inside color	0
max iterations	255
escape value	4.0
parameter file	tricorn
palette	parula
source	Tricorn.hpp

Time (mean ± σ):     575.8 ms ±  21.6 ms    [User: 528.1 ms, System: 36.5 ms]
Range (min … max):   536.0 ms … 602.0 ms    10 runs

Multicorn

Parameters


Generator	Z_bar^exp + C
exponent	4
inside color	0
max iterations	255
escape value	4.0
parameter file	multicorn
palette	viridis
source	Mandelbrot.hpp

Time (mean ± σ):      1.316 s ±  0.016 s    [User: 1.261 s, System: 0.040 s]
Range (min … max):    1.293 s …  1.346 s    10 runs

Barnsley Fern

Parameters


Generator (xn)	xn = xx * x + xy * y + xc (see below)
Generator (yn)	yn = yx * x + yy * y + yc (see below)
inside color	128
max iterations	10000000
parameter file	barnsleyfern
palette	green
source	IteratedFunctionSystem.hpp

Generator

Probability	Transformation [ xx xy yx yy xc yc ]
p < 0.01	[ 0.000 0.000 0.000 0.160 0.000 0.000 ]
p < 0.86	[ 0.850 0.040 -0.040 0.850 0.000 1.600 ]
p < 0.93	[ 0.200 -0.260 0.230 0.220 0.000 1.600 ]
p < 1.00	[ -0.150 0.280 0.260 0.240 0.000 0.440 ]

Time (mean ± σ):     664.8 ms ±   9.4 ms    [User: 621.5 ms, System: 33.5 ms]
Range (min … max):   648.1 ms … 676.3 ms    10 runs

Barnsley Fern (Culcita)

Parameters


Generator (xn)	xn = xx * x + xy * y + xc (see below)
Generator (yn)	yn = yx * x + yy * y + yc (see below)
inside color	128
max iterations	10000000
parameter file	culcita
palette	green
source	IteratedFunctionSystem.hpp

Generator

Probability	Transformation [ xx xy yx yy xc yc ]
p < 0.02	[ 0.000 0.000 0.000 0.250 0.000 -0.140 ]
p < 0.86	[ 0.850 0.020 -0.020 0.830 0.000 1.000 ]
p < 0.93	[ 0.090 -0.280 0.300 0.110 0.000 0.600 ]
p < 1.00	[ -0.090 0.280 0.300 0.090 0.000 0.700 ]

Time (mean ± σ):     637.9 ms ±  32.5 ms    [User: 583.6 ms, System: 33.9 ms]
Range (min … max):   589.1 ms … 683.9 ms    10 runs

Barnsley Fern (Thelypteridaceae)

Parameters


Generator (xn)	xn = xx * x + xy * y + xc (see below)
Generator (yn)	yn = yx * x + yy * y + yc (see below)
inside color	128
max iterations	10000000
parameter file	thelypteridaceae
palette	green
source	IteratedFunctionSystem.hpp

Generator

Probability	Transformation [ xx xy yx yy xc yc ]
p < 0.02	[ 0.000 0.000 0.000 0.250 0.000 -0.400 ]
p < 0.86	[ 0.950 0.005 -0.005 0.930 -0.002 0.500 ]
p < 0.93	[ 0.035 -0.200 0.160 0.040 -0.090 0.020 ]
p < 1.00	[ -0.040 0.200 0.160 0.040 0.083 0.120 ]

Time (mean ± σ):     572.3 ms ±   8.5 ms    [User: 533.0 ms, System: 31.7 ms]
Range (min … max):   562.6 ms … 590.9 ms    10 runs

Sierpinski Carpet

Parameters


Generator (xn)	xn = xx * x + xy * y + xc (see below)
Generator (yn)	yn = yx * x + yy * y + yc (see below)
inside color	128
max iterations	10000000
parameter file	sierpinski-carpet
palette	sand
source	IteratedFunctionSystem.hpp

Generator

Probability	Transformation [ xx xy yx yy xc yc ]
p < 0.125	[ 0.33 0.00 0.00 0.33 -0.66 0.66 ]
p < 0.250	[ 0.33 0.00 0.00 0.33 0.00 0.66 ]
p < 0.375	[ 0.33 0.00 0.00 0.33 0.66 0.66 ]
p < 0.500	[ 0.33 0.00 0.00 0.33 -0.66 0.00 ]
p < 0.625	[ 0.33 0.00 0.00 0.33 0.66 0.00 ]
p < 0.750	[ 0.33 0.00 0.00 0.33 -0.66 -0.66 ]
p < 0.875	[ 0.33 0.00 0.00 0.33 0.00 -0.66 ]
p < 1.000	[ 0.33 0.00 0.00 0.33 0.66 -0.66 ]

Time (mean ± σ):     429.3 ms ±  31.5 ms    [User: 402.7 ms, System: 18.1 ms]
Range (min … max):   393.0 ms … 472.3 ms    10 runs

Sierpinski Triangle

Parameters


Generator (xn)	xn = xx * x + xy * y + xc (see below)
Generator (yn)	yn = yx * x + yy * y + yc (see below)
inside color	128
max iterations	10000000
parameter file	sierpinski-triangle
palette	inverted gnpu
source	IteratedFunctionSystem.hpp

Generator

Probability	Transformation [ xx xy yx yy xc yc ]
p < 0.33	[ 0.50 0.00 0.00 0.50 -0.50 -0.50 ]
p < 0.66	[ 0.50 0.00 0.00 0.50 0.00 0.50 ]
p < 1.00	[ 0.50 0.00 0.00 0.50 0.50 -0.50 ]

Time (mean ± σ):     377.3 ms ±  26.8 ms    [User: 353.2 ms, System: 16.8 ms]
Range (min … max):   350.7 ms … 432.0 ms    10 runs

Other Examples

Tree

Parameters: tree

Seaweed

Parameters: seaweed

Julia (Dragon)

Parameters: julia-dragon

Julia (Siegel Disk)

Parameters: julia-siegel

Julia (Flower)

Parameters: julia-flower

Mandelbrot (Histogram coloring)

Parameters: mandelbrot-histogram

Chrysantemum (Julia)

Parameters: chrysantemum

Cross Snowflakes

Parameters: cross-snowflakes

Crystal

Parameters: crystal

Dendrite (Julia)

Parameters: dendrite

EKG (Julia)

Parameters: ekg

Snowflakes (Julia)

Parameters: julia-snowflakes

Sine (Julia)

Parameters: julia-sin

Cosine (Julia)

Parameters: julia-cos

Dragon Curve

Parameters: dragon-curve

Julia (1/z|Conjugate)

Parameters: julia-funcs

Julia (c * fn(z))

Parameters: julia-func

Julia 6

Parameters: julia6

Koch Curve

Parameters: koch

Koch Triangle

Parameters: koch-triangle

Koch (Mix)

Parameters: kochmix

Leaf

Parameters: leaf

Leaf 2

Parameters: leaf2

Levy Curve

Parameters: levy-curve

Mandelbrot (Sine)

Parameters: mandelbrot-func

Mandelbrot (Sqr|Cos)

Parameters: mandelbrot-funcs

Mandelbrot (1/z^4)

Parameters: mandelbrot-reciprocal

Maple

Parameters: maple

Pascal Hadamard

Parameters: pascal-hadamard

Pentagon

Parameters: pentagon

Mandelbrot sinh^2(z)

Parameters: sinh

Snowflakes

Parameters: snowflakes

Tree 2

Parameters: tree2

Newton

Parameters: newton

Newton IV

Parameters: newton4

Barnsley Tree

Parameters: barnsleytree

Biomorphs

Biomorph M (Mandelbrot)

Parameters: biomorph-mandelbrot

Biomorph 1 (Julia)

Parameters: biomorph-julia

Biomorph 2 (Julia)

Parameters: biomorph-julia2

Biomorph 3 (Julia)

Parameters: biomorph-julia3

Biomorph 4 (Julia)

Parameters: biomorph-julia3

Biomorph 5 (Julia)

Parameters: biomorph-julia5

Biomorph 6 (Julia)

Parameters: biomorph-julia6

Biomorph 7 (Julia)

Parameters: biomorph-julia7

Biomorph 8 (Julia)

Parameters: biomorph-julia8

Files

README.md

Latest commit

History

README.md

File metadata and controls

GitHub Repository

Building (Unix/Linux)

Usage

Required parameters

/PARAMS={parameters.json} or /PARAMETERS={parameters.json}

Optional parameters

/IMAGE={image.png}

/PALETTE={palette.json}

/BENCHMARK

Other parameters

/INVERTX

/INVERTY

/INVERT

/LOG

/NORMALIZED

/MOD

/HISTOGRAM

/DEFAULT

Examples

Mandelbrot Set

Parameters

Benchmarks

Newton

Parameters

Julia Sets

Common Parameters

Specific Parameters and Benchmarks

Mandelbrot4

Parameters

Burning Ship

Parameters

Burning Ship (2)

Parameters

Burning Ship (3)

Parameters

Tricorn

Parameters

Multicorn

Parameters

Barnsley Fern

Parameters

Generator

Barnsley Fern (Culcita)

Parameters

Generator

Barnsley Fern (Thelypteridaceae)

Parameters

Generator

Sierpinski Carpet

Parameters

Generator

Sierpinski Triangle

Parameters

Generator

Other Examples

Tree

Seaweed

Julia (Dragon)

Julia (Siegel Disk)

Julia (Flower)

Mandelbrot (Histogram coloring)

Chrysantemum (Julia)

Cross Snowflakes

Crystal

Dendrite (Julia)

EKG (Julia)

Snowflakes (Julia)

Sine (Julia)

Cosine (Julia)

Dragon Curve

Julia (1/z|Conjugate)

Julia (c * fn(z))

Julia 6

Koch Curve