Al-Andalus

The geometry of the Alhambra.

The Alhambra in Granada is the western edge of the Islamic world and the most complete room-by-room survival of its geometry. The Nasrids who built it, the last Muslim dynasty in Iberia, left dados of cut-tile mosaic so exact that the walls read as proofs. This is the Andalusi style, and it is where the studio's western tradition begins.

FIG. 1 - The Comares register, drawn live. An eight-fold star-and-cross field of the kind that lines the Nasrid dados, coloured by congruence class.

The Nasrid style

Nasrid Granada ran from 1238 to 1492, and for those two and a half centuries its workshops perfected alicatado: glazed tiles cut to shape by hand and set into mosaic. The dados of the Comares Hall are its signature, star-and-cross fields and interlocking polygons where the rule is absolute, no two tiles that touch may carry the same glaze. There is no painted shortcut here. Each colour is a separate cut piece, so the pattern and the palette are the same act.

The bones and the crescents

The Alhambra also holds two patterns you will find almost nowhere else, and they are the reason it belongs on a page about mathematics. Both are curved cut-tile: the hueso or bone tiling, a checkerboard of interlocking bone-shaped tiles, and the crescent tiling, a chiral field of hook-shaped tiles with no mirror at all. In each, every curved edge is a true circular arc struck from a single compass opening. A wall of pure curves, and still, provably, compass-and-straightedge. That is the whole claim of this studio, and the Alhambra made it first.

FIG. 2 - The Alhambra bone tiling, in a plaster-and-glaze register. The curved tiles themselves are the pattern; there is no overlaid line network.

Derived, not generated

Everything the studio draws in the Nasrid register comes out of the construction, not off a photograph: the star-and-cross from its underlying tessellation, the bone and the crescent from one compass radius each, coloured by class the way a cutter fills a panel. Derived, not generated. The Alhambra is where that discipline is easiest to see, because the walls are still standing and the geometry is still exact.

THE ALHAMBRA, IN ONE SENTENCE - the Nasrid cut-tile mosaic of Granada, star-and-cross fields plus two rare curved cut-tile patterns whose arcs are all struck from a single compass setting, the western high point of Islamic geometry.

Read on

The bones of the Alhambra: curved cut-tile geometry The hueso in full: how a pattern with no straight edge stays pure compass work, every arc from one setting.

Draw an Alhambra dado yourself.

Build the Nasrid star-and-cross, the bone tiling and the crescent, recolour by class and export print-ready files - free in the browser.

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Common questions

What is the geometry of the Alhambra?

It is Nasrid geometric ornament, the tilework of the last Muslim dynasty of al-Andalus, worked mainly as alicatado, hand-cut glazed tile set into mosaic. The dados of the Comares Hall and the Court of the Myrtles are star-and-cross fields and interlocking polygon patterns, coloured so that no two touching tiles share a colour. The Alhambra also carries two rare curved cut-tile patterns, the hueso (bone) and the crescent, whose arcs are still exact compass work.

What is alicatado?

Alicatado is the western Islamic technique of cutting individual pieces of glazed tile to shape and setting them into geometric mosaic, the same craft as Moroccan zellige. Each shape is a separately cut piece of fired ceramic, not a pattern painted onto a square tile. The Alhambra dados are alicatado, and so is most of the tilework of Fez and Marrakesh.

Is the Alhambra the same as Moroccan zellige?

They are the same craft, alicatado cut-tile mosaic, worked either side of the Strait of Gibraltar in the same centuries. The Nasrids of Granada and the Marinids of Fez shared masons, motifs and palettes, so a Comares dado and a Bou Inania dado are close cousins. The studio treats them as one western tradition and lets you recolour a pattern from either register.