Quasicrystal Lab visualizes quasicrystal interference patterns — structures that exhibit long-range order without periodic repetition. Unlike regular crystals with translational symmetry, quasicrystals display forbidden symmetries (5-fold, 8-fold, 12-fold) that were thought impossible before Dan Shechtman's Nobel Prize-winning discovery in 1982.
The shader generates quasicrystal patterns by superposing plane waves at rotationally symmetric angles. For 5-fold symmetry, five cosine waves oriented at 72° intervals are summed — their interference creates the Penrose-tiling-like pattern with local 5-fold rotational symmetry but no translational period. The pattern contains both thick and thin rhombus regions arranged aperiodically, matching the geometry of Penrose tiles.
Interactive controls adjust wave count (5, 7, 8, 12-fold symmetry), frequency, phase animation speed, and color mapping. Higher wave counts produce increasingly complex aperiodic tilings with richer structure.