Diffusion Limited Aggregation is a Java applet which simulates the creation of a coral like structure. Each yellow dot on the screen is moving until it hits the growing coral formation, which initially starts with a single point (the red one in the middle).
The original location of this page is at: http://www.kclee.de/clemens/java/dla/
There is a much faster version of this applet (thought you can't observe the moving dots that nicely).
Source code: DLAApplet.java
For the impatient, here are some images: