He didn’t know what he was looking for the first time he walked into the Alhambra. You come in from the heat and the light hits the walls and for a moment you just stand there, your mind doing something it doesn’t have words for yet.
That was 1922. Escher was twenty-four years old, recently graduated. The Moorish artists who made these walls had been dead for six centuries. They had left no notes. No theory. Just the walls.
He came back in 1936. Some things you have to see twice.
What the artists in the Alhambra had discovered — without algebra, without proof, working in a tradition that forbade them from drawing a single living creature — was that there were exactly seventeen ways to tile an infinite plane with a repeating pattern. The Russian mathematician Fedorov would articulate this formally in 1891, centuries after the fact, the way mathematics sometimes chases art home and explains what it already knew.
Escher took the problem and made it harder. He asked: what if the edge between two tiles is also the outline of a fish? What if the sky is made of birds and the birds are made of sky? He would move a single line and the whole system would tremble. He did this for years. Revision after revision, in small notebooks, by hand.
There is a word for what he was doing. We just didn’t have it yet.
The word is algorithm.
An algorithm is a set of rules, followed in sequence, to solve a problem. We think of them as things that live in machines, in data centers drawing enough power to light a city. We think of them as fast. Escher’s algorithm was not fast.
He would begin with a grid. Hexagons, maybe, or the interlocking diamonds of a pattern he had traced from the Alhambra walls. Then he would ask the question that made everything hard: what lives here? Not what shape — what creature? What thing with a spine and a purpose and an outline that a human eye would recognize before the brain caught up?
The constraint was absolute. Every point on every edge had to satisfy two animals simultaneously. Change one line and you changed everything downstream, the way a single altered fact in a long investigation suddenly makes you reread everything you thought you knew.
He failed constantly. The notebooks are full of it. Half a lizard becoming nothing. A bird whose wing destroyed the fish below it. He would back up and try again, the way you back up on a road that has stopped being a road.
He was doing, neuron by neuron, what a diffusion model now does in milliseconds.
But here is the thing about milliseconds. They don’t leave notebooks.
