A small collection of interactive simulations exploring how complex, emergent behavior arises from simple local rules. (under construction)

• Percolation

  Randomly occupied cells on a lattice — does a connected cluster span the grid? Below a critical occupation probability the clusters stay small and isolated; above it one cluster suddenly reaches all the way across.

  
• Forest Fire

  Trees grow, lightning strikes, fire spreads. The Drossel–Schwabl model self-organizes to a critical state with no characteristic fire size, so the distribution of burn sizes follows a power law.

  
• Abelian Sandpile

  Grains topple when a pile gets too tall, cascading into avalanches with no characteristic size. The original example of self-organized criticality, and the source of some very striking fractal patterns.

  
• Brownian Motion

  Random walkers in one dimension and two. A large ensemble drives the statistics while a handful of individual paths are drawn — watch them spread as the square root of time, end against an absorbing wall, or stream sideways under a field.

  
• Reaction-Diffusion

  Two chemicals on a lattice you draw on: one feeds the other, which catalyses its own production. Spots, stripes and mazes come out of a single reaction — the Gray-Scott model, and Turing's mechanism for how a uniform mixture decides where to put its pattern.