The Game With No Players

Four short rules and a grid of cells produced patterns that move, multiply and compute. Whether that is order or only the appearance of it is harder to say.

Abhishek Leela Pandey26 Oct 20261 min readGRE2 questions ↓
A grid of black and white squares in which a small diagonal cluster of cells drifts across the page leaving an empty trail behind it.

In October 1970 Martin Gardner described in Scientific American a pastime devised by the mathematician John Conway. A grid of cells, each either alive or dead, updates in steps according to four brief rules about the number of living neighbours a cell has. Nothing else is specified and no one makes any move, which is why Conway called it the Game of Life. Within weeks a team led by Bill Gosper found a pattern that emits moving shapes without end, and later work showed that the grid can simulate any computation. For some starting patterns, therefore, no known shortcut predicts the outcome without running the rules and watching. Simple rules, it seems, do not guarantee simple outcomes, although the rules alone do not explain why anyone should find the outcomes meaningful.

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