Interactive demonstrations -
Stephen Wolfram's systematic exploration of 1D cellular automata revealed that simple rules can generate complexity rivaling anything in nature. Each cell's next state depends on its current state and its two neighbors, creating 2³ = 8 possible configurations. With 2 possible outputs, there are 2⁸ = 256 possible rules.
View the cellular automaton evolution in 3D space, where time becomes the vertical axis. Each layer represents a generation, creating a volumetric pattern that reveals long-term structures.
Explore the entire space of elementary cellular automata. Featured rules (bold border) include historically significant patterns discovered by Wolfram and others. Click any rule to view it in the Evolution tab.
Create custom rules by defining the output for each of the 8 possible neighborhood configurations. Click the output bits below to toggle them (white = 0, black = 1) and create your own cellular automaton rule.
Analyze emerging patterns, detect repetitions, and identify common structures.
Measure the information content and randomness of patterns over time. High entropy indicates chaotic behavior (like Rule 30), while low entropy suggests order (like Rule 90's Sierpiński pattern).
Examine the patterns in frequency space using 2D Fourier transforms. Regular patterns show clear frequency peaks, while chaotic rules show more distributed spectra.
Wolfram Elementary Cellular Automata Explorer
Version 2.0 (System.css Edition)
A comprehensive tool for exploring all 256 rules of Stephen Wolfram's elementary cellular automata.
Features include real-time evolution, 3D visualization, pattern analysis, entropy measurement,
and Fourier analysis.
Part of the CCAB (Claude Code and Algorithmic Beauty) collection.
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