Interesting things happen at the boundary between order and chaos, where the qualities of both states are evident. There is enough order to retain information, and enough chaos to provide variety. Many complex dynamic systems, including life itself, seem to naturally evolve towards this "edge of chaos", where adaptation, problem solving, and evolution by mutation and selection are all exhibited. A good way to explore this interesting phenomenon is to study a famous cellular automaton called "Conway's Game of Life" which inhabits the edge of chaos region. The Game of Life is famous for demonstrating "emergent complexity" - how elaborate patterns and behaviors can emerge from very simple rules. This screensaver allows you to understand and explore the edge of chaos through the Game of Life.
See also: emergent complexity, Edge of Chaos, cellular automaton, Game of Life, Conway, CA