Conway's Game of Life: the simplest universe that learns to compute.

John Horton Conway, then a young fellow at Gonville and Caius College, spent the late 1960s looking for the simplest possible rules that could produce unbounded complexity. He was responding, in part, to John von Neumann's earlier work on self-replicating cellular automata, which required dozens of states per cell and rules of intimidating length. Conway wanted something a child could memorise. After roughly two years of pen-and-paper experimentation with friends and graduate students, he settled on a two-state, eight-neighbour grid governed by three sentences.

A live cell with two or three live neighbours survives to the next generation. A dead cell with exactly three live neighbours becomes alive. Every other cell dies or remains dead.Conway's three rules, 1970

The Game of Life was published in October 1970 by Martin Gardner, in the Mathematical Games column of Scientific American. Within weeks readers had begun to mail in patterns. Within months Bill Gosper, working at the MIT AI Lab, had constructed the glider gun: an arrangement that produces an endless stream of moving spaceships, settling Conway's open question of whether the system could grow without bound. Gosper's discovery is sometimes counted as the first proof that a finite seed in a deterministic two-state grid can give rise to genuinely unbounded structure.

Berlekamp, Conway and Guy, in the 1982 book Winning Ways for your Mathematical Plays, sketched the proof that the Game of Life is Turing-complete: a sufficiently large pattern can simulate any computation that any digital computer can perform. Later constructions by Paul Rendell and others built actual Turing machines inside the grid; constructions by Andrew Wade, in the late 2000s, produced patterns that replicate themselves entirely from Game of Life primitives. The two-page rule set, with no further input, is computationally universal.

Conway's Game of Life sits at the head of a long lineage. Stephen Wolfram's classification of one-dimensional cellular automata in the 1980s extended the idea downward in dimension; Karl Sims' evolved virtual creatures, in 1994, extended it upward into three dimensions and fitness landscapes; Bert Chan's Lenia, published in 2019, generalised the discrete grid into a continuous field with smoothly varying neighbourhoods. Each step reinforces the original observation: complex, life-like behaviour does not require complex rules, only patient substrate.

For Runaric, this is the foundational lineage. Every petri we run descends from Conway's bet, that complexity does not need to be designed if the substrate is patient enough. The axis Life takes the bet to its embodied conclusion: not just universal computation in a flat world, but agents whose policies were not written by a human, exported from the grid, and asked to live in a real one. Conway's contribution was not the rules. It was the demonstration that a small set of local laws is sometimes all the world is.