Islamic · 9th century CE · Girih & Arabesque

Islamic
Geometry

Fold symmetry. Interlocking stars. A mathematics that tiles the infinite plane without repetition — discovered in Baghdad nine hundred years before Western science named it.

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Zone I — Origin & meaning

The Alhambra, Baghdad, Cairo. One mathematics.

Islamic geometric art emerged in the 9th century CE as a response to a theological and aesthetic challenge: how to create visual art of transcendent beauty without depicting the human form. The answer was mathematics — the most abstract, universal, and eternal of languages.

This collection's mathematical roots trace to the House of Wisdom in 9th-century Baghdad, where scholars translated Euclid's Elements into Arabic — geometric knowledge that shaped architectural ornament across the Islamic world for centuries afterward, from tilework to the inlaid marquetry still produced in Damascus today.

"The craftsman who designed the Alhambra's tile patterns understood, intuitively and practically, mathematics that Western science would not formalise for five hundred years. The geometry is the theology."

Each piece here is built on the 4.8.8 tiling — regular octagons and squares arranged so every vertex meets one square and two octagons, a construction that recurs across Islamic architecture from Marrakech to Isfahan. Around it, star motifs are generated from a chosen fold symmetry — the same compass-and-straightedge logic long used in girih strapwork ornament, executed here algorithmically rather than by hand.

Islamic · 9th century CEGirih strapworkAlhambra · Isfahan · Cairo4.8.8 tilingFold symmetry
Zone II — The mathematics

The 4.8.8 tiling & fold symmetry

Fold symmetry sets how many points radiate from each star's center — the same value repeated as the pattern extends across the tile. Combined with the 4.8.8 octagon-square tiling beneath it, this produces a fully periodic construction: one that repeats regularly and precisely, the way traditional Islamic tilework was designed to extend across an entire wall or floor without gaps.

// Islamic star motif
Points: P_k = (R·cos(k·2π/n), R·sin(k·2π/n))
Star: connect every s-th point, s = floor(n/3)
// Periodic 4.8.8 tiling · fold symmetry 5–12
Tiling
4.8.8
octagons + squares
Fold symmetry
5–12
selectable
Origin
9th c.
House of Wisdom, Baghdad
Repetition
periodic, infinite extent
Zone III — Your sandbox

Enter the tile

A unique Islamic geometry computed now. Change fold symmetry between 5-fold and 12-fold. Zoom in to watch the sub-pattern emerge inside the tile.

Level 1 — The Tile
One complete girih unit. Perfect fold symmetry.
At zoom levels 2–4: drag to explore
Custom colours
Palette presets
Seed: IG-0000-xxxx
Current design — seed: IG-0000-xxxx
This pattern exists nowhere else

Your Islamic geometry was generated at this moment from a unique seed. Download the image and share it wherever you like.

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