TITLE: SPIN LATTICE — an Ising playground
PROMPT: Build 'SPIN LATTICE', an Ising-model playground as op-art: a grid of dots whose spin up/down renders as warm/cool halves of a two-tone rotation, slowly flipping under temperature; magnetization meter, temperature slider, live flip-rate readout; the ensemble visibly orders below the critical point (dots align) and melts above it. Layout: the lattice as a centered tapestry with instrument rails; palette: bone background, ink and vermilion dots. Interactions: temperature slider (critical point marked) changes behavior live; click any dot to pin its spin; a QUENCH button drops temperature instantly to watch domains freeze; sweep mode animates temperature up and down while plotting the magnetization curve on a small canvas graph. Real physics, hypnotic, museum-plaque explanations.
DESCRIPTION: A working 2-D Ising simulation staged as museum op-art. A 56×56 periodic lattice of two-tone discs — vermilion half over ink half — rotates 180° on every spin flip, so the ensemble reads as shimmering static above T꜀ and locks into aligned op-art stripes below it. Real Metropolis dynamics run in-page on a checkerboard update with precomputed Boltzmann acceptance thresholds; the magnetization meter, live flips-per-second readout, and a plotted |m| versus T curve (dashed Onsager T꜀ marker at 2.269) all derive from the same simulation state. Museum plaques explain the wager, the exact critical point, and your instruments; ink-and-bone palette with hard offset shadows keeps it a printed object, not a screensaver.
TECHNIQUES: Typed-array spin/pin state (Int8Array/Uint8Array) with periodic indexing; checkerboard Metropolis sweeps with exp(-ΔE/kT) acceptance table; cubic-eased per-dot rotation for flip animation scaled by temperature; DPR-aware canvas tapestry with save/translate/rotate two-tone disc rendering; small-canvas order-parameter plot with dashed T꜀ guideline and live tracer dot; frame-budgeted physics accumulator; pointer painting of pinned seed spins; temperature sweep oscillator driving both the thermostat slider and the curve sampler; prefers-reduced-motion honoured (instant flips, slower physics cadence).
INTERACTION: Temperature slider (T꜀ ticked in vermilion) reshapes dynamics live; click or drag on the lattice pins spins as domain seeds; QUENCH flash-freezes to watch domains race; SWEEP breathes T up and down while plotting |m|(T); RESET re-rolls the ensemble; flip-rate and magnetization instruments update continuously.