3 species

What is this?

Conway's original "Game of Life"

John Conway's famous "Game of Life" is not a "game" in the traditional sense. It is a cellular automaton meant to very simply (and unrealistically) simulate the development of a population of cells. Each cell behaves according to the following simple rules:

  1. Any live cell with fewer than two live neighbours dies, as if caused by under-population.
  2. Any live cell with two or three live neighbours lives on to the next generation.
  3. Any live cell with more than three live neighbours dies, as if by overcrowding.
  4. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

(Conway was a British mathematician, hence the spelling of "neighbours")

Cells with more neighbors will appear brighter and cells with fewer neighbors will appear darker. (This was not part of the original game of life, but I've included it to help illustrate how the cells interact.)

2 species variation

This version uses for two interacting populations of cells, and two addition rules:

  1. When a cell dies due to overcrowding from more than 5 neighbours, a new cell of the other species will take its place.
  2. When a cell is brought to life by exactly three neighbors, it will kill an overlapping cell of the other species.

In most cases, the replacement colonies will die off quickly, but occasionally, the conditions will be just right for this new cluster of cells to thrive.

3 species vartiation

This version works similarly to the 2 species variation, except now, each species can only generate a cell of one species, and only kill a cell of the other. Think "Rock Paper Scissors".

  • green overtakes blue
  • red overtakes green
  • blue overtakes red

So what do I do?

"Run"/"Stop" will let you toggle whether or not the game is running, "Step" will allow you to see a single step from the current configuration of cells, and "Clear" will kill all the cells on the screen. You can add or remove cells by clicking. Try making your own starting configuration of cells and seeing how those cells "evolve" over time.

Want to find out more? Here's a video fromNumberphilewith John Conway himself describing the genesis of his famous &quote;game&quote;.