Discover the mathematics of pattern and repetition through 24 interactive demonstrations. Draw inside kaleidoscopes, paint wallpaper groups, grow Penrose tilings, and construct Islamic geometric art -- all powered by the deep structure of symmetry groups.
See also: Group Theory for the abstract group axioms behind every symmetry pattern, Lie Groups for continuous symmetries of physical systems, and Hyperbolic Geometry for tilings of the hyperbolic plane that classical Euclid forbids.
Interactive kaleidoscope drawing with dihedral group symmetry
The 7 frieze groups: translations, reflections, and glide reflections
Paint a motif and watch it tile the plane in all 17 wallpaper symmetries
Platonic and Archimedean tilings with interactive vertex figure explorer
Aperiodic kites & darts with inflation, deflation, and matching rules
Star polygons, rosette construction, and compass-and-straightedge geometry
Deformable tiles that morph between shapes while preserving tessellation
Cut-and-project method, forbidden symmetries, and diffraction patterns