gumowski-mira attractor

Here's an unusual chaotic attractor: the web doesn't seem to have much information on this one, except that it was invented to model particle trajectories in physics. A google image search for 'mira fractals' does turn up some pretty results though.

The system seems to give interesting results only when b is close to one. It behaves less chaotically when b > 1 is fixed, so you can actually animate it - click the thumbnail to see.

ikeda map

Continuing the theme of strange attractors, here's the well-known one embedded in the Ikeda map. The thumbnail at left shows the central 'vortex' of the attractor, and links to a larger viewport.

In these images, I've plotted the real and imaginary components along the x and y axes respectively. But the more popular way to visualize this attractor adds an extra parameter to the system and is expressed in trigonometric functions. Such adaptation of the code below yields these results.

hénon attractor

French astronomer Michel Hénon reported on this strange, fractal attractor in 1976. Since then, it has been among the most studied examples of chaotic dynamical systems.

martin attractor

This pattern generator, discovered by Barry Martin, was nicknamed 'Hopalong' when Scientific American introduced it in their September '86 issue.

Clicking the window adjusts the viewport position; there is also an alternate version with color and animation.

Also, for a certain Rubyist friend, I wrote another lazily-evaluated, colored and animated implementation in Ruby.