Symmetry (reflection, radial, tiling) turns a small motif into a full frame at minimal cost

Symmetry operations are very cheap computationally — they require only absolute-value folds, polar modulo, or coordinate modulo — but produce a rich sense of structure. Reflection folds one coordinate by its absolute value. Radial/kaleidoscopic symmetry converts to polar coordinates, quantizes the angle into N wedges, and reflects within each. Tiling takes coordinates modulo a cell size so one drawn cell paints the whole plane. All three operate in the coordinate domain before any drawing. The aesthetic lever is the choice of symmetry group: bilateral reads as calm or figurative, high-order radial reads as ornamental or hypnotic, none reads as raw and generative.

Examples

A single sdf-shape under kaleid(6) fills the frame with 6-fold symmetry from one primitive. The mood changes from decorative to raw by removing the kaleid.

Assessment

Name three symmetry operations and their coordinate-domain implementation. Describe how the choice of symmetry group affects perceived mood.