After I watched Collatz Conjecture in Color - Numberphile, I was inspired to try visualizing the Collatz Conjecture myself. I was also keen to finally try out some Houdini!
I first tried to generate the strands using a VEX Detail Wrangle node, but unfortunately the VEX compiler crashed when I wanted to make use of arrays in structs. I instead used the Python node inside the Geometry SOP to generate the tree. Below are the results!
Thanks to Numberphile for the inspiration and @pixelkram for showing me some of the Mantra renderer features.
Download: collatz.hiplc (Houdini Indie 16.0.569)