- These images are generated using a small program I wrote in Processing. They use simple epicycles of periodic functions (think about the moon going around the earth going around the sun) that are increasing at small but proportional increments. Here I incremented the functions millions of times by factors > 0.01. The expected image in a pure mathematical sense would follow the main brightest white line infinitely.
This result is obtained, though, due to the way computers do math (floating point). When you add a very small number to a very large number, sometimes the result is truncated to a number that is very close to but not exactly the result of the addition requested. As the incrementation became very large the small increments began to be inexact and they diverged from the pure increment at an accelerating rate. Eventually the result of the addition became so large that the entire increment was truncated and the drawing halted.