Rule 30 Cellular Automaton
1D cellular automaton showing chaotic behavior. Used in Mathematica's random number generator. Middle column appears random. Rule 30: 00011110 in binary.
Visualization
Interactive visualization for Rule 30 Cellular Automaton
Rule 30 Automaton:
- • Elementary cellular automaton
- • Produces chaotic patterns
Interactive visualization with step-by-step execution
Implementation
1class Rule30 {
2 private rule: number[] = [0, 1, 1, 1, 1, 0, 0, 0]; // Rule 30
3
4 generate(width: number, generations: number): boolean[][] {
5 const grid: boolean[][] = [];
6 let current = new Array(width).fill(false);
7 current[Math.floor(width / 2)] = true; // Single cell
8
9 grid.push([...current]);
10
11 for (let t = 1; t < generations; t++) {
12 const next = new Array(width).fill(false);
13
14 for (let i = 0; i < width; i++) {
15 const left = i > 0 ? current[i - 1] : false;
16 const center = current[i];
17 const right = i < width - 1 ? current[i + 1] : false;
18
19 const pattern = (left ? 4 : 0) + (center ? 2 : 0) + (right ? 1 : 0);
20 next[i] = this.rule[pattern] === 1;
21 }
22
23 current = next;
24 grid.push([...current]);
25 }
26
27 return grid;
28 }
29
30 generateRandom(steps: number): number[] {
31 const width = 2 * steps + 1;
32 const grid = this.generate(width, steps);
33 return grid.map(row => row[Math.floor(width / 2)] ? 1 : 0);
34 }
35}Deep Dive
Theoretical Foundation
1D CA: each cell depends on itself + 2 neighbors = 8 patterns (2³). Rule number encodes output for each pattern. Rule 30 = 30₁₀ = 00011110₂. Produces pseudo-random center column despite deterministic rules. Class 3 behavior (chaotic).
Complexity
Time
O(w×t)
O(w×t)
O(w×t)
Space
O(w×t)
Applications
Industry Use
Pseudo-random number generation
Cryptographic applications (historical)
Monte Carlo simulations
Procedural content generation
Chaos theory demonstrations
Pattern generation in art and design
Testing randomness in algorithms
Use Cases
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