flacle / collatz

Arc diagram visualization of the parity Collatz function from the famous conjecture.

Collatz 2-Adic Parity Map

Clockwise arc diagram visualization of the parity reformulation of the Collatz function
from the paper 2-adic parity explorations of the 3n+1 problem.
 
This example shows the orbit of the parity map 25 -> 38 -> 19 -> 44 -> 11 -> 26 -> 13 -> 20 -> 5 -> 8 -> 1.

Features

1. Show or hide differences between increments or decrements of n_{t} - n_{t-1} (edgeLabels = True/False)
2. Show or hide nodes on the number line (hideNodes = True/False)
3. Diagrams can be saved/displayed as either SVGs or PNGs

General Info

1. Language: Python 3
2. Dependencies:
   1. mpmath
   2. math
   3. drawSvg
   4. functools

License

This project is licensed under the terms of the MIT license.

Reference

• Laclé, F. 2-adic parity explorations of the 3n+1 problem (2021)
  https://hal.archives-ouvertes.fr/hal-03201180/document