A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on the states of neighboring cells. The rules are then applied iteratively for as many time steps as desired.

mathworld.wolfram.com/CellularAutomaton

To generate an elementary cellular automaton, use

```
ca = CellularAutomaton(rule, init, gen)
```

where `rule`

is the Wolfram code (integer), `init`

is a vector containing the initial starting condition and `gen`

is the number of generations to be computed.
For a single starting cell in the middle just omit the `init`

vector.

To generate 15 generations of elementary cellular automaton of rule 90 use

```
using CellularAutomata
ca90 = CellularAutomaton(90, 16)
```

```
#
# #
# #
# # # #
# #
# # # #
# # # #
# # # # # # # #
# #
# # # #
# # # #
# # # # # # # #
# # # #
# # # # # # # #
# # # # # # # #
# # # # # # # # # # # # # # # #
```

For a more complex cellular automaton you can change the number of states `k`

the cell can be and the radius `r`

of neighbors that can influence the states.
If `k`

is changed to be larger than 2, a totalistic CA is computed where only the average value of all neighbors count.
This can be done like this

```
ca = CellularAutomaton(993, 15, k=3)
```

```
X
XXX
X# #X
X X
XXX XXX
X# #X X# #X
X # X
XXX ### XXX
X# #X # X # X# #X
X # X # X
XXX ## X ## XXX
X# #X # X # X# #X
X X### XXX ###X X
XXX X XX # # XX X XXX
X# #X XX###X## ##X###XX X# #X
```

Two dimensional cellular automaton (like Conway's Game of Life) can be created by

```
ca = CA2d(B, S, init, gen)
```

where `B`

and `S`

are vectors that have the numbers of neighboring cells that define when cell is born or survives, `init`

(matrix) is the initial starting condition and `gen`

is the number of generations the CA is to be computed.

Game of life is then run for 9 generations for e.g. a turbine pattern by typing

```
ca = CA2d([3], [2, 3], init, 9)
```

1st step

```
###### ##
###### ##
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## ##
## ##
##
## ######
## ######
```

2nd

```
####
# # ##
# # #
## #
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# # # #
# # ##
# ##
# # #
## # #
####
```

3rd

```
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####
# ## ## #
## #
## ## ###
#### # ###
# # # #
### # ####
### ## ##
# ##
# ## ## #
####
##
```

4th

```
# #
#
##
# ## #
# # #
# # ###
# #
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# # #
# ## #
##
#
# #
```

5th

```
##
#
### ##
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# # ##
# #
## # #
# # ###
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#
##
```

6th

```
##
#
# # ##
# # ### #
# ######
## ##
###### #
# ### # #
## # #
#
##
```

7th

```
# # #
## # ###
# #
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# #
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```

8th

```
## ## #
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#
##
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##
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```

9th

```
###### ##
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##
## ######
## ######
```

To run tests, execute the following command from the root folder of the repository:

```
julia tests/run_tests.jl
```

12/23/2013

19 days ago

41 commits