Cellular Automaton Explorer

What is a Cellular Automaton?

A cellular automaton is a grid of cells that evolve over time according to simple rules. Each cell looks at itself and its neighbors to determine its next state. Time flows downward, with each row showing a new generation.

Rules

Each rule (0-255) defines what happens for each of the 8 possible neighborhood patterns. The binary representation of the rule number specifies the output for each pattern.

Notable Rules

Rule 110 - Proven Turing complete. Watch for 'gliders' that move across the grid.
Rule 30 - Chaotic behavior. Used by Mathematica for random numbers.
Rule 90 - Creates the Sierpinski triangle fractal pattern.
Rule 184 - Models traffic flow. Try with random initial conditions.

Boundary Conditions

  • Periodic: Edges wrap around (like a cylinder)
  • Fixed (dead): Cells outside are always 0
  • Fixed (alive): Cells outside are always 1
  • Reflective: Edges act like mirrors
Comparing:
Rule 110
Rule 30

Rule 110

01101110

Description

Turing complete rule with complex behavior.

Properties

  • Proven Turing complete
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