The committee had spent three years trying to tile the lobby floor.
Not literally three years. Two weeks for the first contractor, who proposed a herringbone pattern and was dismissed. One month for the second, who proposed hexagonal marble and was dismissed. Then the committee entered what Lucinda privately called the philosophical phase, where the question was no longer which tiles but what tiling meant.
"The pattern should reflect our values," said the chair, who valued regularity.
"A repeating pattern implies we've already said everything we're going to say," said the vice-chair, who valued novelty.
They compromised on a Penrose tiling — ordered but never repeating. Two tile shapes, a handful of rules, and a pattern that would cross the entire lobby floor without ever producing the same local arrangement twice. Every section would look like it belonged. No section would be a copy of any other.
The contractor they hired specialized in aperiodic installations. He arrived with a portfolio and a caveat.
"The thing about Penrose tiles," he said, "is that you can't assemble them locally. If you just follow the matching rules tile by tile, you'll eventually back yourself into a corner — a configuration where no legal tile fits. The only way to guarantee the pattern works is to already know the whole thing."
The committee looked at each other.
"But we don't know the whole thing," said the chair.
"Nobody does," said the contractor. "In practice, you work from a large enough initial seed and trust the rules. When you hit a dead end, you back up. Sometimes quite far."
They approved the project. The work took four months. The lobby filled with gold and blue rhombi — thick diamonds catching the morning light, thin ones receding into shadow. From the mezzanine you could see the five-fold symmetry radiating from the center, each spoke carrying its own grammar of shapes.
On the day of the unveiling, Lucinda arrived early and walked the floor alone. She noticed something the contractor hadn't mentioned. At the edges, where the pattern met the walls, several tiles had been cut. Not dramatically — just trimmed to fit the rectangular boundary. The aperiodic pattern, which theoretically extended forever in all directions, had been given edges.
She knelt at one of the cuts. A thick rhombus, its amber surface catching the light from the skylight above. One corner ended cleanly at the wall. The other three corners reached toward tiles that reached toward other tiles that reached toward the center.
The pattern didn't know it had been cut. That was the thing. Locally, every tile obeyed its matching rules. Globally, the pattern extended forever. But here, at this wall, the forever had been trimmed to fit the room, and the tiles on either side of the cut continued as though the cut hadn't happened.
She stood up and looked across the floor. Five thousand tiles, no two arrangements identical, all following the same handful of rules. The order was real. The order was also local. And the wall was where the local met the actual, and one of them gave way.
She thought about the committee meetings. How the question had been what the floor should say. How the answer, in the end, was a pattern that said the same thing everywhere without ever repeating itself.
She walked to the center and looked down. Ten tiles radiating from a single point. A sun that the contractor had placed first, before any of the others, because everything else needed to know where it was.
The sun didn't look special. It was just tiles — the same shapes as every other tile, following the same rules. But remove it, and the pattern couldn't exist. It was the seed. Not the most important tile. The first one placed, so that the others could begin to make decisions.
She looked up at the skylight. Then back at the floor.
Somewhere near the east wall, a janitor had already placed a rolling bucket on three of the tiles. The bucket sat there with the calm authority of something that didn't know it was standing on a mathematical object. The tiles supported it without commentary.
Lucinda went to get coffee.