 1. |
Any live cell with fewer than two live neighbors dies, as if by loneliness. |
| 2. |
Any live cell with more than three live neighbors dies, as if by overcrowding. |
| 3. |
Any dead cell with exactly three live neighbors comes to life. |
Conway's Life is a cellular automaton. Prof. It consists of a plane of cells that can be either alive (occupied) or dead (unoccupied). At each tick of the clock, the cells are queried and updated according to the three rules above. The time sequence of configurations that results is deterministic. The only "variable" is the starting configuration.
A more complete introduction Life may be found in Martin Gardner's Mathematical Games column on this subject that appeared in the October 1970 issue of Scientific American. The text of this article is available here.
Prof. Laughlin's implementation of Life is intentionally simple. It is written in javascript and can be downloaded just by fetching the html source. The implementation is relatively slow (javascript is interpreted) and uses periodic boundary conditions (i.e. is a torus). The torus may be enlarged by increasing the value of "n" on line 16. The simulation may be sped up by decreasing the argument (presently set to "333") on line 204.
The starting configurations on the implementation's menu fall into two broad categories. The first, called "oscillators", generate patterns that change with time but repeat. The repeat time ranges from 2 clock ticks (Blinker) to 138 ticks (Gabriel 138). The second, called "gliders", generate patterns that, while oscillating, also translate, so that the pattern drifts steadily with time. Large gliders are called "spaceships". Other, more interesting configurations, such as breeders, puffer trains and glider guns, are omitted for space reasons.
None of the designs, omitted or included, is self-evident. All were discovered over time by dedicated hobbyists and all were surprises. This process continues today. Most of the starting configurations that you can imagine simply die out - either by disappearing altogether or by becoming constant in time. Others proliferate out of control in the infinite plane.
There are extensive Life resources on the Internet. The following sites are especially important:
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Mark D. Niemiec's Life Page | |
Paul Callahan's Page of Conway's Life Miscellany | |
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Stephen Silver's Life Lexicon | |
David Eppstein's Life Page | |
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Achim Flammenkamp's Life Page | |
Jason Summers's Life Page |