I provided a maths professor called Steven Strogatz with an animation. It was for one of his articles within his column in the New York Times. Stevens column is an excellent read for people. He explains advanced mathematics for any layperson that has an interest in maths from basic to baffling. This particular article covers complex numbers and explains how they solve problems regarding square roots and negative numbers. It is an excellent read even if you only have a basic understanding of maths and its called “finding your roots” Click here to read it.
This is the animation I made for him. This fractal is based on using Newton’s method to solve 1 – z^3, with the colouring based primarily on which root of the equation is found, and secondarily on how long it took to find it.
The depth of this zoom is e14 – Note that the three different colors meet together in infinitely many different places, and wherever two of the colors meet, the other color always joins them.