Method  /  Generative Assets · Wave VII — Chance

How Brownian was made

A GPU field of 65,536 pollen motes, each kicked by independent Gaussian noise every frame. One mote is traced in gold; a side plot measures the crowd's mean-square displacement rising in a straight line — the moment randomness turns into the law that weighed the atom.

Robert Brown's 1827 puzzle — pollen that jitters in still water for no visible reason — is the seed of the atomic theory. Einstein's 1905 paper showed the jitter is water molecules bombarding the grain at random, and that the grain's mean-square displacement must grow linearly with time, ⟨r²⟩ ∝ t. The site's single job is to let a viewer see both halves at once: the incomprehensible chaos of one grain, and the ruler-straight law hiding in the average. The audience is anyone who likes the idea that panic, repeated enough, becomes physics.

Argued from the subject: dark water, pale motes, one gold thread. The mote colour is a line/mark token; body copy uses a dedicated high-contrast ink so nothing small ever sits on the bright accent.

• Sora

  Display and body. A geometric sans with an even, technical texture — light weights at large sizes give the headline a clean, instrument-panel calm that suits a physics demo.

• Space Mono

  All readouts, labels and figures. The fixed-width digits make the ⟨r²⟩ counter and step tally read as live measurement, not decoration — the typographic conceit that the page is an instrument.

• GPGPU sim

  three.js GPUComputationRenderer ping-pongs a 256×256 float texture — 65,536 mote positions — through a Langevin step shader. Each texel draws two Gaussian kicks (Box–Muller from hashed noise) per frame and wraps toroidally, so the field stays uniformly dense and shimmering with no CPU cost.

• Render

  A Points cloud whose vertex shader samples the computed position texture; additive blending on dark water gives the storm its glow. Orthographic camera sized to the viewport aspect.

• Traced walk

  One reflecting-boundary walker recorded into a 1,500-point ring buffer, drawn as a vertex-coloured Line that fades from deep to bright gold, with a soft head dot at the live position — the signature tangle.

• MSD plot

  A canvas-2D ensemble of 520 free walkers computes ⟨r²⟩ each step and plots it against the analytic line ⟨r²⟩ = 2·s²·n. Single walks are noise; the average is dead straight — the whole point, made measurable.

Hardening throughout: DPR capped at 2, sized to the container, resize-debounced, rAF paused on document.hidden with a clamped delta on resume, a WebGL context-loss fallback (static gradient + a still MSD plot), and a reduced-motion path that primes one settled frame and never starts the loop.