Chaos theory and its little cousin – strange attractors – have been around for a long time. Pictures of chaotic systems and strange attractors abound, and they are a mainstay for computer math experimentalists, although still in the minor leagues relative to the Mandelbrot set. Most implementations tend to ignore the fact that these systems [...]

In the past year, I’ve experimented with different ways to visualize non-Euclidean tessellations.  Mainly, I’ve made movies with simple zooms or animations. But sometimes I think I want something more interactive, so that viewers can explore tessellations as they wish, as opposed to watching them fly by. Last year, I dabbled with creating some ways [...]

There’s something about music or a soundtrack that really enhances what would otherwise be just a silent movie. So I plan to add music to my visualizations as time and inspiration allow. Here’s an example that I did a week or two back. The original movie was 24 seconds long, but now it’s been slowed [...]

A few weeks ago I discovered noteflight.com, a website that lets you create musical scores.  I’ve always wanted to use scoring software, but never got around to it until – well you know, the price was right. Years ago I wrote a computer game called Boulder Dash.  The music for that was composed in a [...]

Just stumbled across this mating movie at Curt McMullen’s site.  I used to play a lot with fractals that were hybrids between quadratic Julia sets.  This is apparently a movie of one of these matings evolving.

I recently saw this classic image from over a century ago attempting to illustrate the limit set of a reflection group. Benoit Mandelbrot computed a more exact version a few  decades ago. Mandelbrot’s version is more correct as far as the limit set goes, but it doesn’t show the tessellation (the white and shaded regions [...]

I just got word that a UK professor was going to show these movies to her hyperbolic geometry class today, as a treat for the last class of the term. Reminds me of when I was in public school and we got ice cream on the last day of school. In another day and age, [...]

Obviously I haven’t been diligent in maintaining this blog. But I’ve made some progress. Much remains to be explained, but I’ve posted a couple of movies at brainjam.ca/hyperbolic that show the kind of thing I’m aiming for. They’ve been made using UltraFractal, which frees me from the tedium of writing my own UI and rendering [...]

I’ve set myself the task of creating a movie that shows a hyperbolic tessellation. This project has been brewing in one form or another for years, but I’ve finally got the time and motivation to at least get started on it. Along the way, we’ll follow background, progress and various tangents. Although the math part [...]