About
Hello —
My son Justin turned six months old, and I started thinking about what to give him. Almost everything you can give a baby is gone within the year. It gets outgrown, or broken, or quietly lost in a drawer. I wanted to find something that would not be.
I am a mathematician, and I have loved Islamic geometric patterns since long before I could say why. They seemed like the right answer. Nobody owns them, nothing about them wears out, and they were true before Justin and will be true after me. But a pattern anyone could have is not much of a gift, so I let the name do the choosing. Arabic letters carry numbers, and the number inside a name is what draws the pattern. His is his.
Yours may not be yours alone, and I think that is the best thing here. Two names that look nothing like each other can add up to the same number and arrive at the same drawing. ياسمين and Yasmin both read 171, and so do plenty of names I have never heard. When it happens they share the page. Nothing is reserved and nobody is turned away, and you may find out who you have been keeping company with.
How it happens
- 1.
A name becomes a number
Arabic letters carry values: ا is 1, ي is 10, غ is 1000. Poets used this for centuries to hide dates inside their lines, so a couplet mourning a building also tells you the year it fell. Latin is transliterated first; Chinese is read as pinyin.
- 2.
The number picks a ground
One of fifteen: the tilings under most historical star patterns, and quasi-periodic grounds that never repeat. Each range of angles was set by looking, so no name lands on an ugly page.
- 3.
The ground becomes a pattern
A point at the middle of every tile edge, two rays out at equal angles, extended until they meet. Neighbouring tiles measure from the same edge, so the strands meet on it exactly and cross unbroken. That is why these feel inevitable rather than assembled.
Every point has coordinates you could work out on paper. There is no image model anywhere near it, and the same name gives the same pattern on any machine, this year or in twenty.
Almost none of this is mine. Hankin worked the method out a century ago by standing in front of the buildings and asking how the lines could have been laid down, and Kaplan later put it in a form a machine can follow. What stayed with me, reading them, was how little it takes. The three steps above really are the whole of it, and everything after them follows. The grounds that never repeat come from de Bruijn, and they belong here because Lu and Steinhardt found the same order in tilework at Darb-i Imam five centuries early. When I am unsure a page has come out right, I hold it against Bourgoin's plates and look.
It will not draw figures, or Qur'anic text, or the divine names. Not out of squeamishness — colouring pages get crumpled and thrown away, and nobody should have to be careful about that. The geometry carries the tradition perfectly well on its own.
Azul is hello in Tamazight, the greeting of the Amazigh of North Africa. It is also, by a long road, the Spanish word for blue — from azulejo, the glazed tile, from the Arabic al-zulayj. A greeting, a tile, and a colour. This makes one of the three.
What I hope for is small. That Justin grows up able to check this for himself, and finds that it holds. And that anyone who prints a page, a child at a kitchen table or a class or somebody with a quiet evening, gets some of the same hour out of it that I got from making it. Print it, colour it, give it away.
— Andrew, at KAUST