In 1970 the mathematician John Conway invented a 'game' that plays itself: a grid of cells, each alive or dead, and four simple rules about how many live neighbours a cell has. Nothing else. Yet out of those rules come shapes that never change, shapes that blink, and shapes that glide across the board, although no rule says anything about moving, at least not explicitly. Only changes from neighbours can translate into and be interpreted as motion. Draw your own cells or pick a pattern, and switch on 'Show what happens next' to see the rules at work on every single cell.
This article and its interactive demo were created with the help of generative AI and editorially reviewed.