Patterns & Tessellation
Repeating geometry from a compass and a straightedge
What it is
Repeating geometric designs built from a small set of shapes and symmetry rules - most famously the star-and-polygon tilings found across Islamic architecture and decoration, historically produced with nothing more than a compass and straightedge.
History
Geometric tessellation flourished across the Islamic world from roughly the 8th century onward, reaching particular sophistication in Persian, Moorish, and Central Asian architecture. The Alhambra palace in Granada, Spain - built mostly in the 13th-14th centuries under the Nasrid dynasty - is one of the most studied surviving examples; mathematicians later found that its walls exemplify all 17 possible wallpaper symmetry groups. In 2007, physicists Peter Lu and Paul Steinhardt proposed that some medieval Islamic tilings, built from "girih" tiles, may have approximated quasicrystalline (Penrose-like) patterns centuries before their mathematical discovery in the West.
Main Contributors
The mostly-anonymous craftsmen and geometers of the medieval Islamic world; in modern scholarship, Peter Lu and Paul Steinhardt for the girih-tile research, and mathematician H.S.M. Coxeter for his work on the symmetry groups underlying such patterns.
Latest Trends
Computational recreation of these tiling systems - parametric pattern generators rather than hand construction - lets the same underlying geometry be explored far faster than by hand. This site's own piece goes a step further, layering a modern reaction-diffusion "dissolve" effect onto historically grounded tiling geometry.