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. You can download a folder of files to generate the fractals. Download Fracton document files colatzf.zip Download FractInt parameter files colatzp.zip
