Last edited 15dec15 by jpbloom2@illinois.edu

# The 3D Chaos Game

## By Joey Bloom

## Abstract

The Chaos Game is a method of fractal image generation. It is a particle system that draws points one by one according to a set of rules, and the points drawn will approach an attractor which may be a fractal. Many well known fractals in the euclidean plane can be produced by the Chaos Game. I developed an RTICA using HTML5 Canvas and Javascript to display these fractals and allow the user to manipulate the initial conditions of the Chaos Game to produce approximations of the attractors of Iterated Function Systems.

## RTICA

Javascript Program

Here is the Real Time Interactive Computer Animation (RTICA) that I developed for my project. It should work in most browsers on most operating systems.

## Documentation

PDF

TEX

Feel free to browse my project documentation. It covers the mathematics behind my RTICA as well as how I went about programming it.

## Proposal

PDF

TEX

Here is my project proposal. I outline the mathematics involved in the chaos game, including affine transformations and iterated function systems. I describe my plans for building my javascript application. I also give references from my research.

# Rotating Hypercube!

Javascript Program

I attempted to turn Greg Tavarres' rotating 3D cube into a rotating 4D hypercube . I'm not sure if it's totally correct, it looks a little wonky. This is not part of my Chaos Game project, this was just for fun.

I researched the algebra for 4D graphics here: http://steve.hollasch.net/thesis/chapter2.html