Vex Spore

Vex Spore turns the mathematics of crystallographic symmetry into a live design canvas. Choose one of the seventeen wallpaper groups — every way a pattern can tile a flat plane — drag a single vertex on your motif, and every symmetric copy updates at frame rate. No render button. No waiting. The group enforces its own rules; you just move points.

Place a polygon in the fundamental domain and the engine tiles the entire plane exactly: rotations, reflections, glide-reflections, and translation lattices all computed from first principles. A symmetry overlay draws rotation centres, mirror axes, and glide lines directly on the canvas so you can see the geometry you are working with. Four colouring modes — single, translation parity, handedness, and coset tint — let you explore how colour interacts with the symmetry of the chosen group.

When your pattern is ready, the Repeat and Yardage screen gives you the rectangular repeat in centimetres, whether it is a straight or half-drop layout, and how many metres of fabric a given bolt width requires. Hexagonal and rhombic groups are handled correctly: the app states the half-drop geometry rather than hiding it. Import a photograph from the camera or photo library and trace its outline into motif vertices. Export the finished repeat tile to your photo library at print resolution.

For the mathematically curious, an Aperiodic screen grows a Penrose P3 tiling by inflation, showing in real time that the tile count multiplies by phi-squared and the thin-to-thick ratio converges to one-over-phi. A built-in Method Sheet derives every number the app displays, and a Glossary defines every term in plain language.