DIRECTORY / SANDBOXES / LANGTONS-ANT.TURING

LANGTON'S ANT AUTOMATON

Deterministic 2D Turing machine building an emergent recurring 104-step highway pattern.

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LANGTON'S ANT HUD

// TURING RULE STRING (L = Left, R = Right)

// CURATED RULE VAULT

SPEED (STEPS/FRAME) 100x

STEP TICKS: 0

[Click on canvas to drop a new Ant at pointer]

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RESEARCH & LEARNING VAULT // Langton's Ant & Generalized 2D Turing Machines

Deterministic cellular automata, the 10,000-step highway transition, and Turing universality.

ACADEMIC & ALGORITHMIC REFERENCE

// HISTORICAL ORIGINS

Invented by artificial life pioneer Chris Langton in 1986. In 2000, Gajardo et al. proved that Langton's Ant is Turing complete.

// GOVERNING EQUATIONS

\text{State}_{t+1} = (\text{State}_t + 1) \bmod N, \quad \theta_{t+1} = \theta_t \pm 90^\circ

// BROWSER IMPLEMENTATION

Executes state transition lookups based on arbitrary user-provided rule strings (e.g. `RL`, `LLRR`, `LRRL`), rotating ant direction and advancing cell states.

// GUIDED EXPERIMENTS TO TRY IN THIS SANDBOX

110k Step Highway Transition

🎯 Action:Set rule to 'RL', speed to 250x, and watch step count reach 10,000.

✨ Observe:After 10,000 steps of pure chaos, the ant suddenly builds an infinite repeating 104-step diagonal highway.

// CURATED PAPERS, RFCS & RESOURCES

Studying Artificial Life with Cellular Automatapaper

By Chris G. Langton (Physica D: Nonlinear Phenomena, 1986)

The original paper introducing Langton's Ant.