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Cellular automata are among the simplest programs. Two such automata are rule 30 and conway's game of life. Conway's game of life is a two dimensional cellular automata calculated on a cartesian grid. Rule 30 is a one dimensional cellular automata.
# Rule 30
One dimensional cellular automata are described in depth by Stephen Wolfram in his book A new kind of science. They function as such, a seed value is given. The common example is one cell activated in the middle of a 1-D grid. Each generation the state of the grid is used to compute the next generation.
In simple 1-D CA there are two possibilities a cell is alive or dead in each generation. The state of the previous generation defines the state of the following generation. The relevant state is the liveness of the previous cell and its left and right neighbor. This yields three boolean values. 23 = 8. There are 8 distinct input states that determine the state of in the following generation. The Rule 30 is one of 256 possible simple 1-D CA Rules. 256 = 28; each rule maps the distinct input states to a boolean representing cell liveness.
The parity between the number of input states and the number of possible rules is no coincidence. Each number between 0 and 255 in binary is the simplest encoding of each rule. The binary for 0 padded to 8 digits is 00000000 this means that for all eight possible input states every output is false. Rule 255 is 11111111 yielding true for all input states. Rule 30 is 00011110 This can be visualized like so.
Rule 0
7
0
6
0
5
0
4
0
3
0
2
0
1
0
0
0
Rule 255
7
1
6
1
5
1
4
1
3
1
2
1
1
1
0
1
Rule 30
7
0
6
0
5
0
4
1
3
1
2
1
1
1
0
0
# Conway's Game of Life
Mathematician and all around genius John Conway devised a cellular automata he named the game of life. The game of life is a two dimensional cellular automata that has very simple rules but produces enough emergent complexity to support structures that can run a universal turing machine.
Surprisingly the game of life is easier to understand than the "simple" 1-D CAs. There is an infinite cartesian grid of cells either alive or dead. Each cell has eight neighbors. The game of life has three rules:
- Live cells with 2 or 3 live neighbors survive
- Live cells with with < 2 or > 3 neighbors will die
- Dead cells with exactly 3 neighbors come to life
# Feeding Rule 30 into Conway's game of life
If you have JavaScript enabled you have been seeing a simulation in the background. This simulation is feeding Rule 30 into Conway's Game of Life. This post is heavily inspired by Cellular Automata: Rule 30 + Conway’s Game of Life