Cruz Godar

Graduate Student
Mathematics Department, University of Oregon
Eugene, Oregon, USA
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.