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Math · Intermediate

Cellular Automata

A row of cells, each on or off, updating by a tiny rule. What could be simpler? Yet such systems produce fractals, chaos, moving creatures and even full-blown computers. Explore Stephen Wolfram's elementary rules and John Conway's Game of Life, model traffic jams with Rule 184, and follow Langton's ant from chaos to order, then watch a sandpile organise itself to the brink of avalanches and see how mild preferences can segregate a whole city.

7 lessons~40 min0/7 complete
1

One Dimension

Rows of cells.

  1. Elementary Rules256 tiny universes
  2. Chaos from OrderRule 30 and Rule 110
2

The Game of Life

Two dimensions and emergent creatures.

  1. Conway’s Game of LifeBirth, survival and gliders
3

Automata in the World

Traffic jams and a wandering ant.

  1. Traffic JamsRule 184 and the flow of cars
  2. Langton’s AntChaos, then a highway
4

Self-Organisation

Sandpiles and segregation: big patterns from local rules.

  1. Sandpiles & AvalanchesSelf-organised criticality
  2. Schelling’s Segregation ModelMild preferences, strong patterns