Licell

Origin

Game of life is a program created by John Conway in 1970. It's my favorite program : it's one of the simplest BUT it is Turing-complete, it basicaly mean that every Turing machine (like a computer) can be create in this kind of system. This cellular automaton is very interseting in a lot of ways.

What is a cellular automaton ?

A cellular automaton is a pogram which work with a grid of cell (1,2,3,... dimensions), each cells have his own state (true/false, alive/dead, 1/2/3,...). For each step in time, the grid will evolve : each cells will change according to his neighborhood. For exemple, here is the 3 rule of the Game of life :

If a cell have 2 neighbors, the cell will remain in the same state the next step
If a cell have 3 neighbors, the cell will be alive at the same state the next step
If not, the cell will die the next step

The most simple cellular automaton is the Rule 30, a 1-dimension cellular automaton. It the first and only 1-dimension automaton which is proven to be Turing-complete.

Rule 30, each row of pixel is a step, and the row below is the step after

Rule 123 after few steps.

Licell

Licell is a little program that I use to travel between all the possibles rules (6561 possibilites for a 2D grid, with 3 possible output : die, stand, create one). It's fascinating how a simple grid like this with few rules can create those amazing patterns. Here is for exemple rule 123 (I named it myself, it have probably have a different name), it creates a growing pattern which look like a pyramid seen from above.