A grid of cells following one rule can produce anything from static patterns to universal computers.
A row of on/off cells, each updating from itself and its two neighbors: 3 bits, 8 inputs, 256 possible rules. Some produce nothing; a few produce everything.
Stephen Wolfram catalogued all 256 one-dimensional rules in the 1980s and found they fall into strikingly different classes. Rule 90 gives a perfect Sierpinski triangle. Rule 30 produces apparent randomness. Rule 110 sits at the boundary, generating structures complex enough to be proven Turing complete.
Switching between Rule 30 and Rule 90 with the same seed gives a fractal vs. apparent noise. The difference between order and chaos can be a single bit in the rule table.
The 2D version: on a square grid, a dead cell with exactly 3 live neighbors is born; a live cell with 2 or 3 neighbors survives; everything else dies.
From four words of logic come gliders, oscillators, and glider guns emitting streams of new objects. Working computers — logic gates, memory — have been built inside Life.
The R-pentomino: 5 cells, 1103 generations to stabilize, producing 6 gliders plus various still lifes and oscillators. The behavior isn't hidden in the rule or seed — it's a property of their interaction across time.
Wolfram grouped elementary automata into four classes. Class I rules produce uniform grids. Class II produces repeating patterns. Class III produces apparent randomness. Class IV sits between II and III, at what Chris Langton called the "edge of chaos," producing localized structures that interact in complex ways.
Class IV rules support computation: too much order and information can't flow; too much chaos and information can't persist.
Rule 110 is Turing complete: a 1D row of cells looking at three neighbors can compute anything any computer can compute.
The lesson of cellular automata: complicated behavior doesn't need complicated rules. Just a rule, a grid, and time.