Conway's Game of Life
Conway's Game of Life is played out on a grid of cells with the "Asteroid" topology (the surface of a torus, where a cell on the right edge is adjacent to a cell on the left edge, and similarly for top and bottom).
Filled cells are "alive." At each "generation," cells remain (live), blank out (die), or are filled (born), depending on their environment. If N counts the number of occupied neighboring cells (each cell is adjacent to, or touches, 8 others), then the fate of each cell is determined by N according to the following rules:
+ A filled cell lives if N is 2 or 3.
+ A filled cell dies if N is either 0 or 1 (isolated) or 4 or larger (crowded).
+ An empty cell is filled (birth) if N is exactly 3.
To understand the rules of Conway's Game of Life, we strongly recommend carefully working through the examples in the Master the Rules window.
It is essential to count the number of neighbors for every occupied cell to find which ones will die from isolation (fewer than two neighbors) or from crowding (more than three neighbors). New births will occur at the next step in cells where there are exactly three neighbors.
Once you are comfortable with the way the rules work, you can explore the infinitely many possibilities for starting the game. The initial world is called "Life." From any initial configuration, or world, pressing Step> moves to the next generation. Likewise, pressing <Step reverses the process. You can step through as many generations as you wish to see. Pressing Run shows the generations in sequence.
There are twelve preloaded worlds:
Of the twelve "Pentominoes," all shapes become uninteresting fairly soon, except for one, which we call the Wild One. Can you guess, before running it, which shape is wild?
"H or Pi" illustrates some of the effects of size, while "A to Z" shows some alphabetic possibilities. "Dueling Darts," "Flat Fives," and "Fives Cross" show some lovely symmetric patterns and perhaps some unexpected futures.
"Glider Gun" and "Perpetual" are worlds with continued creation.
You can create your own world, either in the regular workspace or in a space with larger squares. To add a cell or to blank a filled cell just click in the square.