What is Golly?
Golly is a cross-platform application for exploring John Conway's Game of Life and other cellular automata. It's also free and open source. More details, including links to the source and binary distributions, are available at the Golly web site:
What is Life?
The Game of Life is a simple example of a set of rules more broadly known as a "cellular automaton", or CA for short. CAs were first studied in the mid-1950s by Stanislaw Ulam and John von Neumann but became much more widely known in 1970 when Conway's Life was described by Martin Gardner in his Scientific American column.
Life is played on an arbitrary-sized grid of square cells. Each cell has two states: "dead" or "alive". The state of every cell changes from one "generation" to the next according to the states of its 8 nearest neighbors: a dead cell becomes alive (a "birth") if it has exactly 3 live neighbors; a live cell dies out if it has less than 2 or more than 3 live neighbors. The "game" of Life simply involves starting off with a pattern of live cells and seeing what happens.
Even though the rules for Life are completely deterministic, it is impossible to predict whether an arbitrary starting pattern will die out, or start oscillating, or expand forever. Life and other CAs provide a powerful demonstration of how a very simple system can generate extremely complicated results.
If you'd like to learn more about Life and other cellular automata then check out the links and books mentioned in the References, or start exploring the Life Lexicon.