Conway’s Game of Life [1] is a zero-player cellular automaton: a lattice of sites, each either alive or dead, that evolves in discrete steps according to a fixed rule applied to every site in parallel. There is no player input during a run: the initial configuration alone determines everything that follows.
At each step, every site looks at its $8$ neighbors (Moore neighborhood) and, writing $n$ for the number of live neighbors, updates according to four rules:
Underpopulation
$n \lt 2$ → dies
Survival
$2 \le n \le 3$ → stays alive
Overpopulation
$n \gt 3$ → dies
Birth
$n = 3$ → becomes alive
Gray sites are alive, black sites are dead; the highlighted site is the one being updated, ringed blue if it is alive after the step or magenta if it is dead.
This simulation runs on an $L \times L$ toroidal lattice with $L = 128$: the edges wrap around, so a glider leaving the right side reappears on the left.
Fill p =
Click toggle site · Ctrl+Click stamp glider · Shift+Click stamp pulsar
References
- M. Gardner, Mathematical Games: The fantastic combinations of John Conway's new solitaire game "life", Scientific American 223, 120–123 (1970). doi:10.1038/scientificamerican1070-120