Home▸Generative Art & Algorithmic Patterns▸K-Fold Rotational Symmetry Drawing Tool (2D)

K-Fold Rotational Symmetry Drawing Tool (2D)

Draw a stroke once and watch it copy itself into K rotationally symmetric sectors on a plain Canvas2D canvas — Rotate mode builds the cyclic group Cₖ, Mirror mode the dihedral group Dₖ, from 1 to 16 folds.

Generative Art & Algorithmic Patterns2DEasy60 FPS📱 Mobile-adapted⇄ 3D version

This 2D companion runs the same rotation-and-mirror math as the 3D version directly on a flat Canvas2D surface: every drawn segment is rotated about the canvas center into K evenly spaced copies (Rotate mode, cyclic group Cₖ), and Mirror mode additionally reflects each copy to build the dihedral group Dₖ with twice as many segments. Pick a fold count from 1 to 16, choose a colour, stroke width and opacity, and draw — the sector guides update live as you change K, and Save PNG exports the finished pattern.

⚙ Under the hood

A plain Canvas2D kaleidoscope drawing tool: every stroke is expanded into K (or 2K, in Mirror mode) rotated/reflected copies about the canvas center using real 2D rotation matrices, matching the cyclic Cₖ and dihedral Dₖ symmetry groups. Segment count and the active symmetry group are read out live.

symmetrykaleidoscopewallpaper groupsrotational symmetrygenerative artdrawing tool

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