A whole set of beautiful fractals can be grown from a few simple matrices. Each rectangle above controls a single matrix. The matrices are applied in random order, to a random starting point. The point wanders around, trailing red dots. The program wanders the point in the background, copying its tracks to the screen occasionally.
Create new rectangles by clicking and dragging, and modify old ones by dragging the odd symbols at their corners. The large rectangle is just for reference-- it's the identity matrix.
Almost any arrangement of three or four rectangles creates a gentle, feathery fractal. Create the serpinski gasket by dragging out three rectangles which each cover one quadrant of the big rectangle.
View the source.
Download the zip.
I wrote this applet back in December of 1997, just as I was learning Java. It is inspired by a similar, but text-based OpenGL program by my UAF Professor Chris Hartman.
Update: in 2002, I wrote a much better tool in C++ for my IFS bounding work.