Rendering Fractals From Scratch

by Cade Brown <me@cade.site>


A personal obsession of mine, explained in depth.

Fractals have interested me since I was very young. I’ve always been fascinated by the idea of self-similarity, and the fact that you can zoom in infinitely on a fractal and still see the same pattern. They seem like a glitch in the universe — given a small and finite set of rules, you can generate seemingly infinite complexity. How does zz2+cz \to z^2 + c create the above image?

These are some various renderings of fractals that I’ve done, using software I’ve written

Software

Videos

Images

FractalRender output

Overview of the Mandelbrot Set
Overview of the Mandelbrot Set

Scepter Valley, Mandelbrot Set
Scepter Valley, Mandelbrot Set

Elephant Valley #0, Mandelbrot Set
Elephant Valley #0, Mandelbrot Set

Elephant Valley #1, Mandelbrot Set
Elephant Valley #1, Mandelbrot Set

3D Prints

Mandelbrot 3D print, made in Blender
Mandelbrot 3D print, made in Blender

Mandelbrot phone case
Mandelbrot phone case

Me demoing fractalexplorer at the Laboratory for Physical Sciences @ UMD
Me demoing fractalexplorer at the Laboratory for Physical Sciences @ UMD

Fractal rendering program on a TI-84 calculator
Fractal rendering program on a TI-84 calculator

Meta

Me at ISEF 2018
Me at ISEF 2018

This is also me, overlooking some nice scenery (note the Mandelbrot tie)

Me at ISEF 2018
Me at ISEF 2018

This is me at ISEF 2018, presenting my work after winning Grand Reserve Champion at SASEF 2018. (note the Mandelbrot shirt)