Cellular Automata and the Game of Life
Cellular automata were first studied by John von Neumann and Stan Ulam. Later,
interest was revived through the work of Stephen Wolfram.
S.Wolfram (ed.), "Theory and Applications of Cellular Automata", World Scientif
S.Wolfram, "A New Kind of Science", (2001)
Game of Life (John Conway)
Consider a 2
dim array of cells (one
example is shown in Fig.3.9).
Each cell can either be dead or alive, which may be indicated according to the
Starting from an arbitrary initial configuration, the Game of Life is played by
changing the states of every cell simultaneously at each time step according to the
Each cell interacts only with its neares
t neighbors ( see Fig.3.9 ).
If a cell is alive, then
a) It dies of "loneliness" if it has 1 or less live neighbors.
b) It dies of "overcrowding" if it has 4 or more live neighbors.
c) It stays alive otherwise.
If a cell is dead, then
a) It b
ecomes alive if it has exactly 3 live neighbors.
b) It stays dead otherwise.
The challenge is to find those initial configurations that lead to interesting patterns
( see Figs.3.10
Fig.3.9. A dark (live) cell has 8 nearest neighbor (n) white (dead) cells.
Fig.3.10. Death of an initial configuration.
Fig.3.11. Evolution toward a stati
Fig.3.12. Example of a