DIRECTORY / SANDBOXES / RULE-110.TURING

RULE 110 TURING AUTOMATON

Stephen Wolfram's Rule 110 elementary cellular automaton and universal computation particles.

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RULE 110 TURING COLLIDER

// ELEMENTARY CELLULAR RULES

8-BIT RULE LOOKUP TABLE: RULE 110

GENERATION SPEED 60 rows/s

CLICK 8-BIT TILES: Forge Custom Rules | RULE 110: Universal Computing Gliders | CLICK CANVAS: Flip Seed Bits

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RESEARCH & LEARNING VAULT // Rule 110 Turing Collider & Elementary Cellular Automata

Wolfram 1D universal computation, glider collisions, and background ether filtering.

ACADEMIC & ALGORITHMIC REFERENCE

// HISTORICAL ORIGINS

In 2004, Matthew Cook proved Stephen Wolfram's 1985 conjecture that Rule 110 is Turing-complete, capable of universal computation via glider particle interactions.

// GOVERNING EQUATIONS

x_i^{t+1} = f(x_{i-1}^t, x_i^t, x_{i+1}^t) = (\text{Rule} \gg (4 x_{i-1} + 2 x_i + x_{i+1})) \land 1

// BROWSER IMPLEMENTATION

Simulates 1D elementary cellular automata by shifting an 8-bit rule bitmask over 3-cell neighborhoods. Renders descending temporal history waterfall and provides an ether-filtering mode to isolate emergent computing gliders.

// GUIDED EXPERIMENTS TO TRY IN THIS SANDBOX

1Glider Isolation via Ether Filter

🎯 Action:Select '01. Rule 110', click '✨ ETHER FILTER: ON', and watch gliders collide.

✨ Observe:The periodic 14-cell repeating background is visually cancelled out, illuminating only the mobile gliders and logical collisions.

// CURATED PAPERS, RFCS & RESOURCES

Universality in Elementary Cellular Automatapaper

By Matthew Cook (Complex Systems, 2004)

The mathematical proof demonstrating Turing completeness in 1D Rule 110.