Mathematical Cartography
The Geometry of Culture
The mathematics of Moroccan zellige and Islamic geometry.
Every zellige mosaic, every carved plaster panel, every cedar lattice in Morocco is built from the same mathematics: compass-and-straightedge construction. A circle divided into 6, 8, 10, 12, 16, or 24 points generates the star pattern. The more points, the more skill required. A 24-fold rosette demands a master — it uses six overlapping squares rotated at 15° intervals. The geometry is the grammar; the craftsman is the poet.
The Six Star Families
Click to expand. Complexity increases left to right. Construction lines show the compass method.
The 17 Wallpaper Groups
Mathematically, there are exactly 17 ways to tile a plane with repeating symmetry. Moroccan craftsmen discovered all 17 through practice, centuries before mathematicians proved it. Here are the most common in Moroccan zellige:
Reading Notes
Why Stars, Not Faces
Islamic art avoids figurative representation in sacred spaces. The star pattern became the dominant decorative language because it is abstract, mathematical, and infinitely extensible. A single motif tiles to infinity — reflecting the infinite nature of God.
The Zellige Tradition
Zellige tiles are hand-cut from glazed terracotta with a pointed hammer (menqash). A master (maâlem) can cut 500–700 pieces per day. Each piece is shaped by eye to fit the geometric template. Fes remains the centre — the same families have cut zellige for six generations.
Dynasty and Complexity
The Marinids (1244–1465) pushed geometry furthest — their medersas in Fes contain the densest star patterns anywhere. The 16-fold rosette on the Royal Palace doors in Fes is attributed to Marinid craftsmen. After them, complexity plateaued. Modern zellige often reproduces Marinid patterns.
A compass. A straightedge. A circle divided into equal parts. From this, an entire visual civilisation. The zellige craftsman in Fes and the mathematician in Cambridge are working on the same problem — only the notation differs. The craftsman solved it first, by seven centuries.
Sources
Star family nomenclature and construction methods from Bourgoin (1879) “Arabic Geometrical Pattern and Design,” Bonner (2017) “Islamic Geometric Patterns,” and Critchlow (1976) “Islamic Patterns.” Wallpaper group classification from Abas & Salman (1995) “Symmetries of Islamic Geometrical Patterns.” Monument attributions from Touri & Benaboud (2011) and UNESCO World Heritage nomination files. Zellige craft data from Fes maâlem interviews and Ministry of Artisanat records.
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