I discovered the art of iterated function systems (IFS) in a course of fractal geometry in the summer of 2015. Having no background in visual arts, this opened up a weird new world of expression to complement my endeavours in music and theatre. I soon developed a new plotting technique for colouring IFS graphs, and presented it in a Bridges 2016 paper.
As a former teacher, I want to challenge the image of mathematics as soulless number-crunching. Math is art, a creative human endeavour like nothing else. At the same time, math is an integral part of our civilization, rather than a remote academic island.
In a time of media scare over algorithms, I want to show the beauty, fun and empowerment of making your own algorithms. I was never good at drawing, but by using math and code I have become a semi-professional artist.
Julia sets of z^2 + c are the prototypical fractals. Their familiarity makes them the perfect examples for demonstrating new visual techniques, which in turn reveal new aspects of the sets themselves.
This short film is a sequel to my Bridges debut of 2016 and continues the quest for new Julia set variants. After a retrospective beginning, the journey proceeds into newer extensions of my IFS overlay graphing method, notably 3D functions. Between the two worlds, an educational interlude with a comic relief breaks the cadence.
In the latter half of the film, two major 3D forms are given special attention. The first is a joining of regular 2D Julias into a stringy crossing, where the “c” parameter varies smoothly along the third axis. (A familiar Julia form can be seen at the beginning of that scene, as the shape starts to expand from a thin slice.) The second is a series of “Julia bulbs”, the Julia sets of a quadratic Mandelbulb.
