A 2D grid of cells, each black or white. Each step, every cell looks at its 8 neighbors and follows two rules: "alive with 2 or 3 neighbors stays alive; dead with exactly 3 neighbors becomes alive". Everything else dies. From this minimal recipe — Conway 1970 — emerge gliders, oscillators, replicators, and computers powerful enough to simulate themselves.
why Life is the canonical emergence
Conway's rules are absurd in their simplicity:
• survive if you have 2 or 3 living neighbors
• be born if you have exactly 3
• otherwise die
From these two clauses emerge: still lifes (block, beehive, loaf), oscillators (blinker, pulsar), spaceships that crawl across the grid (the glider; LWSS; HWSS), guns that produce a stream of spaceships forever (the Gosper glider gun), eaters that consume incoming spaceships, and ultimately — logic gates, memory, clocks, and finally universal computation.
Paul Rendell built a Turing machine in Life (2002). Adam Goucher built a programmable computer in Life (2010). Nicolas Loizeau built a Life pattern that simulates Conway's Game of Life inside itself. The implication is breathtaking: any program, including this entire web page, could in principle run on a sufficiently large Game of Life board. Life is Turing-complete with a 2-state, 8-neighborhood, deterministic local rule. It demonstrates that computational universality is generic, not exotic.
Click Acorn — a tiny seed of 7 cells. Watch it sputter, then explode into a 1,057-cell pattern over 5,206 generations before settling. The unpredictability isn't randomness; it's the depth of the consequence chain. The rules are deterministic, but the long-term behavior is effectively unknowable except by running it.