Geometry and tilings

Lozenge Tilings

random lozenge tilings of a hexagon, exact by coupling from the past

A study in motion and form.

Studio tab: Lozenge
Implementation family: lozenge
Preset configurations: 7
Recorded evidence: Checks within stated limits

This evidence label refers to recorded internal checks within their stated limits. Sample renders illustrate a configuration’s output. They do not establish scientific validity.

Lozenge Tilings, Arctic circle, a = b = c = 40 preset sample — Arctic circle, a = b = c = 40Sample render

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7 of 7 preset stills available.

Preset gallery.

7 named configurations in this technique. Select an image to inspect its full sample above.

Lozenge Tilings: Arctic circle, a = b = c = 40 preset render — Arctic circle, a = b = c = 40

Lozenge Tilings: Skewed hexagon, the ellipse preset render — Skewed hexagon, the ellipse

Lozenge Tilings: Stack of cubes, a = b = c = 11 preset render — Stack of cubes, a = b = c = 11

Lozenge Tilings: Flattened box, wide frozen wedges preset render — Flattened box, wide frozen wedges

Lozenge Tilings: Fine, a = b = c = 48 preset render — Fine, a = b = c = 48

Lozenge Tilings: Tall box, a = b = 20, c = 40 preset render — Tall box, a = b = 20, c = 40

Lozenge Tilings: Frozen versus free preset render — Frozen versus free

All 7 preset names

Arctic circle, a = b = c = 40
Skewed hexagon, the ellipse
Stack of cubes, a = b = c = 11
Flattened box, wide frozen wedges
Fine, a = b = c = 48
Tall box, a = b = 20, c = 40
Frozen versus free

Keep exploring.

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Hyperbolic Turing

reaction-diffusion on a {p,q} tiling

Explore 7 presets ↗

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Schramm-Loewner Evolution

the random curve of critical two-dimensional systems

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Rotor Routers

rotor-router aggregation and internal DLA

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