About

For Justin

For my son Justin, six months old, born here in Saudi Arabia. I wanted to give him something from this place that will still be true when he is old enough to check it.

How it works

1. 1.

   A name becomes a number

   Arabic letters carry values: ا is 1, ي is 10, غ is 1000. This is ḥisāb al-jummal, used for centuries to hide dates inside lines of poetry. Latin script is transliterated first, and Chinese is read as pinyin.

2. 2.

   The number picks a ground

   One of fifteen families: the tilings under most historical star patterns, and quasi-periodic grounds that never repeat.

3. 3.

   The ground becomes a pattern

   Hankin's polygons-in-contact. A point on the middle of each tile edge, two rays out at equal angles, extended until they meet. Neighbouring tiles share the edge, so the lines cross it unbroken.

Every point has coordinates you could work out on paper. No image model is involved, and the same name gives the same pattern on any machine.

Sources

• E. H. Hankin, The Drawing of Geometric Patterns in Saracenic Art (1925).
• Craig S. Kaplan, “Islamic Star Patterns from Polygons in Contact”, Graphics Interface (2005).
• N. G. de Bruijn, “Algebraic theory of Penrose's non-periodic tilings”, Indagationes Mathematicae (1981).
• Peter J. Lu and Paul J. Steinhardt, “Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture”, Science (2007).
• Jules Bourgoin, Les Éléments de l'art arabe (1879).

What Azul will not draw

Geometric and vegetal forms only. No figures, no Qur'anic text, no divine names: colouring pages get crumpled and thrown away.

The name

Azul is Amazigh for hello. It is also, by way of azulejo and Arabic al-zulayj, the Spanish word for blue.