Elementary Cellular Automata

In mathematics and computability theory, an elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors.

How to interact: Watch as simple rules create complex patterns. Each row shows one generation, with time flowing downward. The pattern starts from a single cell at the top.

Rule numbers: Elementary cellular automata are numbered 0-255 based on their behavior. Different rules produce wildly different patterns:

• Rule 30: Chaotic, used for random number generation
• Rule 90: Creates Sierpiński triangles
• Rule 110: Turing complete (can compute anything!)
• Rule 184: Models traffic flow

These simple systems demonstrate how complex behavior emerges from simple local rules, relevant to physics, biology, and computer science.