Cruz Godar
My first two college courses were in the departments of math and
computer science, and since then, I’ve been fascinated by where the
two subjects meet. Over the past few years, I’ve written dozens of web
applets for creating and exploring fractals and similar objects, and
eventually I developed a JavaScript library to streamline the process
for myself and others. The kind of generative art these applets
produce is a great way to counter the stereotypical presentation of
math as a completely obscure subject, and my hope is for them to be
both useful to mathematicians and aesthetically appreciable by anyone,
mathematician or not.
The most commonly popularized fractals are two-dimensional, but 3D
fractals are entirely possible — drawing them just presents a few
more challenges. The Mandelbrot set cannot be translated
canonically to three dimensions, since there is no appropriate
number system analogous to $\mathbb{C}$, but in 2010, Daniel White
and Paul Nylander managed to use spherical coordinates to produce
something spectacular in its own right, showing just what 3D
fractals could be and igniting the search for more. This image was
taken from an applet written with a custom raymarching engine — an
uncommon rendering algorithm that’s ideal for fractals. The applet
itself allows users to explore the inside of the fractal along
with the associated Juliabulbs.