Sunday, January 18, 2009

Billiard balls and fractals

Virtually any non-stable dynamic system may be used for generating of fractal images. Here is one example, based on ideal planar billiards.
Consider ideal billiard, consisting of round balls, moving and colliding without friction in the rectangular box.
Then let us measure, how much time needs first ball (green one at the picture) to get to the right wall. Below are the images, showing how time until wall collision depends from initial ball velocity. Horizontal and vertical coordinates at the picture plane correspond horizontal and vertical components of the initial ball velocity, color shows, how much time needed ball to reach the right wall. All pictures are 800x600, about 600K

The top-level view of the fractal

Slightly zoomed
High zoom with different color map
Another highly zoomed image

Increased number of balls. Image became more chaotic. Also, different color map chosen.