Game of Life still revealing secrets

Researchers have found a pattern in Conway’s Game of Life that exhibits startling timelessness...
20 January 2022


The Game of Life was invented in 1970 by mathematician John Conway as a very simple model of how a theoretical population of cells might behave. Now, over half a century later, we are still discovering fantastic behaviours of this straightforward game.

Conway’s Game of Life, or just “Life” as it is often called, is an example of a zero-player game. That means that once you lay out the board, it plays itself according to a very simple set of rules.

The game of life is played on an infinite square board, much like chess or checkers. Each square of the board can have a living cell in it. Then, each second, the board changes. If a living cell has fewer than two neighbours, though, it dies of loneliness; more than three and it dies of overcrowding. If there are exactly three cells bordering an empty square, a new cell is born.

Though the rules are very simple, the Game of Life is known for creating complex and fascinating patterns. Small self-sustaining colonies of cells form patterns that behave like tiny organisms, walking across the board. Other configurations explode like fireworks or flash like traffic lights.

Ville Salo and Ilkka Törmä are two researchers from the University of Turku in Finland, who’ve been looking into the game to try to find some order in the chaos.

Almost immediately after it was invented, mathematicians started finding “still lives”. These are patterns of living and dead cells that never change: each cell hanging in perfect balance with exactly the right neighbours to stay that way.

But there was always the question of the reverse. If still lifes are configurations of cells that don’t change as you go forward in time, can you go the other way? Are there configurations that couldn’t have come from anything except themselves?

John Conway asked if these configurations existed back in 1972. Now, half a century later, we have an answer. Salo and Törmä have found a pattern with this property.

The result is very regular and quilt-like. In fact this was expected and the pair specifically looked for their solution in sections of infinite patterns. To search through all these quilts, they employed a computer program called a SAT solver. After only three and a half hours it struck gold.

After their discovery of the configuration, Törmä and Salo posted the result to an online forum dedicated to the Game of Life. It wasn’t long before it had been verified and other consequences of its existence were discovered.

And so now we know. In a world with stunning complexity and emergent behaviour oases of timeless calm. A small community of cells, living peacefully as they must have, ever since the very beginning.


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