3.1.4. Cellular Automata and the Game of Life

chatventriloquistAI and Robotics

Dec 1, 2013 (3 years and 6 months ago)

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3.1.4.

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
ic
(1986)

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
following table:


Dead

Alive

Value

0

1

Color

White

Black


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
following rules:

1.

Each cell interacts only with its neares
t neighbors ( see Fig.3.9 ).

2.

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.

3.

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
-
12 ).


Example 3
-
2:

The One
-
Out
-
Of
-
Eight Rule
:

Mathematica

files:


03
-
2.nb

Example 3
-
2.nb



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
onary pattern.



Fig.3.12. Example of a

blinker


pattern.