Pentagon Lattice Lab — Z₂ Orientation Cover

Click a tile to inspect. Press edge keys to walk. Press space to play/pause CA, n to step.

Drag to pan · Scroll to zoom · Click a pentagon to select

Lattice

Polygon type: Radius (BFS depth):

Sheet group:

Display

Color mode: Palette: Selected sheet opacity: 0.92 Other sheets opacity: 0.28 Saturation: 60 Lightness: 56 Border width: 1.3 Fill tiles Stroke borders Show only selected sheet Show origin crosshair Background gradient

Labels

Tile center labels (sheet·orient) Edge labels (1–5) Show depth on tile Show tile index Labels on all sheets (not just selected) Label size: 10

Selection

Selection glow Neighbor link dashes Glow strength: 14

Cellular Automaton

Show CA overlay Rule family: B/S rule: Preset: States:

Seed pattern: Random density: 0.30 Speed (steps/sec): 8 Click to paint cells (instead of selecting)

gen: 0

population: 0

by sheet: —

Selected Tile

No tile selected.

Walk History

About

Centroids and vertices live in Q(√5)². Rotations by 72° are exact via cos(72°) = (√5−1)/4, sin(72°) = √(10+2√5)/4 (the radical is stored symbolically as S72 with S72² = (10+2√5)/16).

For general n-gons, floating-point arithmetic is used with double precision. The Sierpiński triangle uses an IFS (iterated function system) with contraction ratio ½.

Docs

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