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 represent dynamics, that they move and evolve. Still pictures can hide the fact that, for example there are sink states, and that was supposed to represent 20,000 iterations only shows 5,000 because the system hit a fixed point at iteration 5,001.
Continue reading “The Sound of Chaos”
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 down to accommodate an atmospheric soundtrack.
Hyperbolic Kaleidoscope from Peter Liepa on Vimeo.
I recently stumbled across this movie of a quadratic mating 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.
To the best of my knowledge, the movie is by Xavier Buff.
I just got word that a UK professor was going to show one of my videos 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, they would have been asked to get out their rulers and compasses and draw the thing, as shown here. Up until recently, that’s representative of the best depiction mathematicians had.
Or watch it on Vimeo.
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 is important, the software part will play a role, because at the moment I’ve got too many choices.