A Cellular automaton is a collection of colored cells on a grid. At each iteration (generation)
the cells may change state (color) depending on the state of the other neighbouring cells.
We will look at automata in which the cells may have 2 states only (dead or alive).
Such simple automata may produce many kinds of interesting behaviour from dull
extinction to life-like growth patterns and chaos.
In the Cellular automata module of Mathgrapher you may try 3 types of automata.
The first 2 (
are taken from the book by S Wolfram entitled "A new kind
of Science". The third one,
is a more general type of automata, sometimes called Life.
Dead (uncolored) cells may come to life and living cells may survive or
die depending on the status of their neighbouring cells. Theinitial
state may be random, or some predefined configuration. Such a configuration
may be drawn and stored under some name (Glider, Gosper_gun, block, puffer,
etc. see the list). You may start with one of these stored configurations by
choosing it from the list. When you start the Game of Life the system evolves
according to the Rule given by 2 numbers. Rule 23 / 3
(Conway's Game of Life)
means that (alive) cells with 2 or 3 neihgbours will survive and dead
cells with 3 neighbours become alive.
More information on Cellular automata:
The second type of automata is a simple two-dimensional one also from
book "A new kind of Science". The inital state is a single black
cell on the middle of a grid of 300x300 cells. Now the color is determined by
the number of black neighbours in the vertical and horizontal direction and by its
present color as follow. For example for the number 942, which is 1110101110 in
binary notation, we have nr of neighbours: 4 3
11 10 10
11 10 meaning that if a cell has 3 neigbours its color will become 10, i.e.
black (1) if it was black and white (0) if it was white. The total number of
recipes will be 1024.