collatz-conjecture

Small program to showcase some properties of the collatz conjecture, also know as 3N+1 problem.

Features:

• Plot a single sequence with given number N

• Plot a single sequence with the y-axis logarithmic scaled to showcase the "randomness" of the conjecture. Also looks like a bad day on the stock market. Also plot the trend to showcase that it is always going down.

• Plot a histogram, which displays how often the first digit of each iteration in a full sequence occurs. This histogram applies to Benfords Law.

• Plot a histogram, which displays the stopping times of a sequence and how often it appears in a full sequence.

• Since the digit counts / stopping times are huge numbers, i calculate them in an c++ function externally, which is then imported to the python script via a shared library (dll). (Because python was too slow for me, even with ctypes and numpy arrays/numbers...)

• Tip: Hold ESC to stop an active calculation!

How to run:

• Option 1: Download the executable version in the respective folder. (Only on x64 Systems with x64 Python)
• Option 2: Clone the repository with

git clone --depth 1 https://github.com/mitsubishievo99/collatz-visualization

and start the script with

python main.py

Dependencies

• numpy >= 1.21.2
• PyQt5 >= 5.12
• pyqtgraph >= 0.12.2