Digital Zellige
Computational geometry meets 700-year-old tessellation — parametric tools for Islamic pattern design
Zellige — the cut-tile mosaic of Morocco — operates on geometric rules discovered by Islamic mathematicians and implemented by Moroccan craftsmen for over 700 years. The patterns are not decorative choices. They are solutions to a mathematical problem: how to tile a plane with no gaps and no overlaps using a limited set of shapes.
The 17 wallpaper groups — the complete set of ways to repeat a pattern in two dimensions — were classified by mathematicians in the 19th century. Islamic artisans had discovered and used all 17 centuries before the formal proof existed. The Alhambra in Granada contains examples of all 17 groups. Moroccan zellige uses a significant subset.
The basic tool is the compass and straightedge. Every zellige pattern can be constructed with these two instruments. The master craftsman (maalem) begins with a circle, divides it into equal parts (typically 8, 10, 12, or 16), and constructs the interlocking star pattern through a sequence of arcs and intersections. The construction is taught by demonstration, not by textbook.
Computational geometry has formalised what the maqlems knew intuitively. Software tools — some developed by researchers specifically for Islamic pattern analysis — can generate zellige patterns from parameters: symmetry group, star order, interlace depth, line width. The patterns produced are mathematically identical to hand-drawn constructions.
The gap between computation and craft remains physical. A computer can design a pattern in seconds. Cutting the tiles — chipping each piece from a glazed square using a sharp hammer (menqash) — still requires years of training. The tiles are cut by eye, fitted by hand, and grouted face-down on a flat surface. The precision is remarkable — tolerances of less than a millimetre across panels of thousands of pieces.
The digital tools serve preservation as much as creation. Damaged zellige panels in historic buildings can be documented, analysed, and reconstructed computationally — ensuring that replacement tiles match the original geometric logic exactly.
Explore the full interactive module — with pattern generators, symmetry group analysis, and the construction geometry animated — at Dancing with Lions: https://www.dancingwiththelions.com/data/digital-zellige
Interactive Module
Data and visualisation by Dancing with Lions
