This page is an exploration of the Collatz fractal. The Collatz fractal has several forms and can be generated by the following equations using complex numbers:

1 - Normal form

z = 0.5 * z * cos(z * pi / 2) ^ 2 + (3 * z + 1) * sin(z * pi / 2) ^ 2

2 - Shortcut form

z = 0.5 * (z * cos(z * pi / 2) ^ 2 + (3 * z + 1) * sin(z * pi / 2) ^ 2)

3 - Simplified normal form from yozh.org

z = 0.25 * (2 + 7 * z - (2 + 5 * z) * cos(pi * z))

For more information on the Collatz fractal see the following web pages.

Wikipedia Webpage

Yozh Webpage

You can download a folder of files to generate the fractals.

Download Fracton document files colatzf.zip

Download FractInt parameter files colatzp.zip

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