Home▸Mathematics▸Tessellation Morph 2D: Polar-Equation Regular-Polygon Tiling

Tessellation Morph 2D: Polar-Equation Regular-Polygon Tiling

2D companion to Tessellation Morph: a lattice of cells traced from the exact polar equation of a regular n-gon, continuously morphing between the {3,6}, {4,4} and {6,3} tessellations while a live readout reports the exact side count, interior angle and area at every frame.

Mathematics2DModerate60 FPS📱 Mobile-adapted⇄ 3D version

Details

CategoryMathematics

RenderingCanvas 2D

DifficultyModerate

Target FPS60

ControlsSliders for morph speed, pulse amplitude, rotation speed and lattice density, plus Reset lattice, Pause and Cycle palette buttons; live n(t), nearest tiling, interior angle and cell/total-area readouts.

regular tessellationpolar equationschläfli symbolinterior angletriangular latticepolygon area

Related simulations

Tessellation Morph (3D original)A 14×14 hex-grid lattice of prisms morphing between hexagonal, triangular and 8-gon cross-sections.

Penrose TilingAperiodic tiling built from two rhombus tile shapes with five-fold symmetry.

Kaleidoscope ShapesMesmerizing kaleidoscope patterns from transformed input shapes. ⊞ All 331 in Mathematics →

This 2D companion replaces the 3D version's per-cell geometry swap with a single continuous formula: the polar equation of a regular n-gon, r(θ) = a / cos((θ mod 2π/n) − π/n), evaluated with a smoothly animated real-valued n. A side panel exposes morph speed, pulse amplitude, rotation speed and lattice density, while a live readout reports the exact current side count, nearest Schläfli tiling, interior angle and per-cell/total area computed straight from that n — so the geometric identity of each frame (triangle, square, hexagon, or an in-between polygon) is always verifiable rather than merely implied by a mesh swap.

⚙ Under the hood

2D regular-tessellation lab driven by the exact polar equation of an n-gon, morphing continuously between the {3,6}, {4,4} and {6,3} tilings with a live Schläfli-symbol, interior-angle and area readout.

regular tessellationpolar equationschläfli symbolinterior angletriangular latticepolygon area

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install