Conway's Life and Related Cellular Automata

I have made a simple program to simulate Life-Like cellular auomata. Click here to play around with it.

These are a family of cellular automata with the following properties:

  • They live on a two dimensional square grid,
  • Each cell is either alive (white) or dead (black)
  • Each step, whether a cell is born or dies depends on how many alive cells are in the eight cells adjacent to it, as well as the current cell state.

The most famous such automata is Conway’s Life, which has the following rules:

  • If a dead cell has three neighbours, it becomes alive
  • If an alive cell has two or three neighbours, it survives; otherwise it dies.

We can label life as B3/S23, meaning that a cell is born if it has three neighbours, and a live cell survives if it has two or there neighbours.

There are 262144 possible Life-like rules. Each can be labelled by a list of of numbers for which a cell is born, and dies. Of these, only a few rules have been explored in any details. Here are some interesting ones to play around with:

Rule Name Description
B3/S23 Life The original ruleset, with highly complex behaviour.
B3/S012345678 Life without Death Exactly what it says on the tin.
B36/S23 Highlife Close relative of Life, with a tendancy to constantly expand.
B35678/S5678 Diamoeba Creates cell-like structures.
B3678/S34678 Day and Night Treats living and dead cells symmetrically.
B4678/S35678 Anneal Close relative of the Ising Model at zero temperature.
B1357/S1357 Replicator Everything eventually replicates.
B3/S01234 Mazes Makes maze-like patterns.

A systematic study of life-like cellular automata can be found here; many further rule sets can be found in this paper.