Five Cellular Automata
To computer scientists and older folks, "The game of Life" doesn't involve a spinner and choices about marriage, but instead a hypnotically pulsating grid. "Life" was one of the first forms of "cellular automata," a way of deriving very complex behaviors from very simple rules. As such, it ushered in a lot of new ways of thinking about science, complexity, and the emergent properties of systems. Also, it let you stare at a constantly shifting computer screen and go "Whoa, dude" a lot.
Cellular automata work by setting an initial condition (dots on a screen) and then rules, such as "if a dot is next to no other dots, it is lonely and dies." From only a handful of such rules, unexpected behaviors and "life forms" emerge--for example, some patterns of dots in Life will "crawl" across the screen, while others form stable patterns that blink on and off.
Five Cellular Automata brings you...five cellular automata, proof that Hermetic Systems believes in truth in advertising. Each has different sets of rules, and many have psychedelic color patterns. The user can set a number of relevant parameters, and either single-step through the process or just let it run. Most automata reach a point of stability fairly quickly.
This isn't a game, per se, as there's no challenge, scoring, or goal; it's an educational toy, especially if you understand the math and rules behind the pretty pictures. It's a good, dynamic, introduction to the principles. The greatest weakness is the inability to draw your own starting positions; this makes it much less useful as a way to experiment with the concepts and discover new behaviors on your own.
Note: Formerly shareware, this software is now freeware.