JavaScript is off, so the live parts of this page are not running. Everything written below is complete on its own and says what each computation does and what it produced — the empty rectangles are where it would have run in front of you. Nothing here needs an account, and nothing is hidden behind the scripts; they compute, they do not reveal.

Moving visuals on this page — measured at 0.26% brightness change per frame and zero flashes per second; your reduce motion setting stops them. What moves, and how it was measured

Mathematical plates that draw themselves — prime counts, orbits and lattices rendered live rather than shipped as pictures. It runs continuously while on screen, and it pauses on its own whenever it scrolls out of view.

We measured it rather than guessing: the largest frame-to-frame change in average brightness is 0.26%, and it produces zero flashes per second against the threshold of three set by WCAG 2.3.1. That is well under the limit, and it is not a promise about any individual: if moving images are a problem for you, you should not have to assess ours.

Everything animated on this site honours your system’s reduce motion setting — turn it on in your operating system or browser and these pages stop moving, with nothing else lost. All the mathematics is in the text and the still figures.

Entry 1 of 7 in Numbers & structure Play with itIllustrative

Conway's Game of Life Numbers & structure

The classic B3/S23 rule (Conway, 1970)

Math: a cellular automaton — a deterministic dynamical system defined entirely by one local rule (Conway, 1970). Dev: the rule itself is a handful of lines; everything you see is real-time canvas rendering via requestAnimationFrame, not a video.

A grid of cells, each alive or dead, updated every tick by three rules: a live cell with 2 or 3 live neighbours survives, a dead cell with exactly 3 live neighbours is born, everything else dies — B3/S23 in the standard notation (Conway, 1970). No randomness after the first frame: every pattern you see below unfolds deterministically from that one rule, seeded fresh each time this panel loads. Our own rule, B37/S2378, runs quietly behind the scenes elsewhere on this site (the faint moving dots on the homepage); this is the classic Conway it grew out of, here in the open, full size, as what it actually is.

Open the full interactive Game of Life — draw your own cells, place gliders and a Gosper gun, run it at your own speed →

Next in this room →The accelerated Collatz map

Back to Numbers & structure · Back to the Notebook

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