Tessellation & symmetry

TESSELLATION SIMULATION

▸ Building the prototile…

▸ Fitting edge-to-edge, checking vertex angles = 360°

▸ Regular · semi-regular · Penrose (aperiodic)…

▸ Computing mirror axes & rotation centers (symmetry group)

▸ Growing the tiles outward from the center…

▸ Ready — Online. ✅

Prototile & parameters

🔷 Prototile

the tile repeated to cover the plane

Tile types—

Vertex configuration—

Fit at vertex—

Symmetry group—

Periodic?—

Tiles · % grown—

Tip

Tiles fit edge-to-edge to cover with no gaps. There are only 3 regular tilings (triangle, square, hexagon) because the interior angle must divide 360°. Penrose covers the plane but never repeats — 5-fold symmetry, the golden ratio φ.

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Switch the Scenario to see 6 tiling types · click a tile to inspect its fundamental domain · toggle symmetry axes & centers

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Tile types · growth progress · drift phase over time tile types% growndrift