
A particularly good animation of Conway's Game of Life
John Conway's "Game of Life" is an exploration of how complexity evolves in nature. It is a game you can play at home, using any board with squares (a chess board is too small, a Go board is better). You lay down any pattern of stones or pieces on the board, and then apply some very simple rules to determine what the next pattern looks like.
If you have the patience to repeat this exercise through many patterns, applying the same rules from one pattern to the next (or better, use a computer) then you will see some strange and wonderful things (as illustrated in this video).
The "Game of Life" is an example of a whole family of investigations into how Nature works, in particular the fascinating study of
Cellular Automata. These show how even very simple rules, repeated many times, can lead to very complex (and sometimes very beautiful) results.
Cellular Automata crop up in a very interesting SF trilogy by
Robert J. Sawyer (who wrote
Flashforward), about the evolution of intelligence in the World Wide Web - if you are interested, I reviewed the books (which start with "Wake")
here.
The "Game of Life" is described
here on my web site.