bismuth

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quasicrystal cousin playground the study

What this is

A bismuth hopper crystal, grown rather than drawn. The seed in the URL fixes everything: the number of masons, their kinetics, the crystal's habit, the oxide palette. Same seed, same crystal, forever — nobody designed it, and share gives you its permanent address.

The masons

Each glowing mote is an agent carrying one brick. It arrives from the melt along a straight line, so it strikes the crystal's outermost corners and edges first. On the surface it random-walks, pulled toward places where a brick would touch more faces, and lays its brick with a probability set by three rules from real crystal growth:

Kossel–Stranski kinetics. A brick touching one face needs a rare nucleation; touching two, it fills at the unit rate; three or more, at once. That is why the walls come out flat and the corners square.
The Berg effect. Supersaturation is highest at a crystal's corners and edges, lowest over the middle of a face — so a face grows as a rim and its centre starves. Every layer is a ring one step further out than the last, and the crystal steps down into its own pit. That is the hopper.
Anisotropy. Six growth-rate weights, one per face normal, decide whether the seed becomes a funnel, a stair, a tower, twins, or a skeletal frame.

If a mason finds no good site, it leaves. It is never forced to lay a brick, and that restraint is what keeps the crystal a crystal.

The colour

Real bismuth is grey. The rainbow is a skin of bismuth oxide a few hundred nanometres thick, and the colour you see is thin-film interference in that skin. This page computes it: the reflected spectrum of air / Bi₂O₃ / metal is sampled at nine wavelengths per pixel and folded through colour-matching curves, so the hue changes with the film's thickness and with the angle you view it from. Bricks laid earlier were hot longer and carry thicker oxide; a brick is laid glowing, cools silver, and only then takes its colour.

Controls

drag to orbit, scroll or pinch to zoom; it turns on its own when left alone
space pause · s skip to the finished crystal · r grow it again
n a new random specimen · ← → the neighbouring seeds
m the crystal as a magnet: diamagnet, ferromagnet, then the field switched off with the magnetization kept · v a section through it, facing you, the field painted on the cut

Quasicrystals

The lattice is the substrate, not the brain: masons only ever choose which site to fill, and the right angles come from the cubic geometry. Swap the geometry and the same laws grow something else. Every specimen has a quasicrystal cousin at /q/<seed>: the same genome on a plane tiling chosen by the seed — Penrose, Ammann–Beenker, a 7-fold quasicrystal, hexagons, kagome and the rest — stacked into prisms. A Penrose substrate gives a decagonal quasicrystal, periodic along its axis and quasiperiodic across it, which is a real class of solid that facets and hoppers like this. The tilings are exact integer complexes (shared with the foam dungeon), so those permalinks are as permanent as the cubic ones. And every specimen has an icosahedral cousin at /i/<seed>: the same genome on the true three-dimensional quasicrystal — space tiled by the two golden rhombohedra, no lattice in any direction — grown as a hollow goblet terraced in the two-fold facets of a rhombic triacontahedron, the habit real icosahedral grains show. It is the biggest tiling the page will build (95,000 rhombohedra), so it takes a few seconds to appear and grows more slowly.

The playground

/lab opens the same engine with the lid off: pick the substrate (any of the ten tilings, or the cubic lattice), paint the initial condition as a height map, rewrite every law of the mason brain, breed or thin the colony, retune the oxide, and release worms — a second wave of agents that tunnel the crystal and take bricks with them. Every playground state is itself a permalink.

The study

/study is what the two agents do to a crystal, measured: masons are a rate and not a front; without recycling every worm wins eventually; the crystal heals bites at its rims and not at its face centres; worms that breed bloom or starve and never cycle; grazers limited to exposed bricks coexist for a long time and then starve on the crystal they smoothed — and the same across tilings.

Everything runs in your browser; nothing is stored. /api/crystal?seed= returns any specimen's brick list as JSON. Part of mino.mobi.