Wolfram Elementary Cellular Automata - CCAB

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Wolfram Elementary
Cellular Automata

Wolfram CA Explorer - All 256 Rules

About Elementary Cellular Automata

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.

Preset Rules

Controls

4 px
50 ms

Statistics

30
Current Rule
0
Generation
1
Active Cells
0%
Density

3D Time Evolution

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.

45°
30°

All 256 Rules at a Glance

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.

50
Loading all 256 rules...

Design Your Own Rule

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.

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Designed Rule Number

Pattern Recognition

Analyze emerging patterns, detect repetitions, and identify common structures.

  • Gliders: Patterns that move across space
  • Oscillators: Patterns that repeat periodically
  • Still Lifes: Stable, unchanging patterns
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Patterns
N/A
Period
0
Complexity

Shannon Entropy Analysis

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).

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Avg Entropy
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Max Entropy
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Wolfram Class

Frequency Domain Analysis

Examine the patterns in frequency space using 2D Fourier transforms. Regular patterns show clear frequency peaks, while chaotic rules show more distributed spectra.

Spatial Domain

Frequency Domain

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Dominant Freq
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Spectral Peak

About

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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