Pick a tiling of polygons and a contact angle, and the lines grow into stars, rosettes and interlaced strapwork, the way the craftsmen of the Islamic world laid them out. Drag the angle to watch the stars open and close, drag the picture to move it, then save it as SVG or PNG.
Pattern
Lines
Colors
Classics
Tip: drag the picture to move the pattern, double-click to center it again. The address of the page keeps the pattern, to share it.
How the patterns are made
Start from a tiling of regular polygons: octagons and squares, dodecagons and hexagons, or simply hexagons. From the middle of every edge, send two lines into each of the two tiles that share it, at the same contact angle from the edge, crossing like an X. Each line runs on until it meets the line coming from the next edge. Do it for every tile, rub out the tiling, and the lines that are left form stars and rosettes, one around each tile, joined by the lines that cross at the edges.
This is the method of polygons in contact, which the British scientist E. H. Hankin worked out in the 1920s from the construction lines he found on Islamic monuments in India and Turkey, and which the computer scientist Craig S. Kaplan described formally in 2005. A small angle makes stars with blunt points, close to the tiling itself; a large one makes slender stars. A gap splits each crossing point in two, for doubled lines.
The lines are then joined into continuous bands and woven, over and under, alternately, all along each band: the interlaced strapwork the Persian tradition calls girih, "knot". It is always possible to weave such a design so that every band alternates, which is why the craftsmen could carve and inlay them without a single break in the rhythm.
Geometric patterns are, with arabesque and calligraphy, one of the three great kinds of ornament in Islamic art, from the Great Mosque of Damascus and the Alhambra in Granada to the tilework of Isfahan, Fez and Samarkand. In tile mosaic (zellige), carved stucco, wood and brass, they were laid out with a compass and a straightedge, and their endless repetition is often read as an image of the infinite.
The tilings are the Archimedean tilings, named by the polygons around each corner: 4.8.8 is a square and two octagons, 4.6.12 a square, a hexagon and a dodecagon. Everything is computed in your browser and drawn as SVG.