Here is the curious thing: the first night I saw the set, it was just wild. The second night, I became used to it. After a few nights, I became familiar with it. It was as if somehow I had seen it before.
Benoit Mandelbrot (20 November 1924 – 14 October 2010)
Pierre had reached the Islands, again. The beach seemed to be white sand, ground infinitely fine and marked by fading footprints. The ocean was a multitude of tones, although he knew his surroundings were as much a product of his interpretation as they were an objective representation of the environment.
He collapsed in the surf and paused to catch his breath. The sun seemed to burn brightly across the islands, and polarized light scattered across the water. He took a moment to admire the rendering. It was different this time, with intricate violet filagree where once there had been sweeping curves. When he was rested, he followed the spiral path to Shishikura.
Pierre had seen Shishikura many times, but the village seemed overwhelmed by changes both subtle and gross. The bamboo groves grew taller, but now the river was little more than a stream. He found Fatou in the orangery, beneath a blazing canopy of glass; he tended the trees as he always did, although this time they grew wild and free, straining at the boundary of their crystal prison.
“Pierre,” he said, unsurprised. “I should have expected you.”
“How long has it been?”
Fatou shrugged. “Perhaps a month, this time.”
“It seems longer to me. Have you seen Julia?”
“You have asked me that many times, and I tell you again now. I never knew a Julia, although perhaps she passed this way before. My memory is not what it was.”
Pierre sighed, although he had expected nothing else.
“Will you stay with us tonight?”
“No,” said Pierre. “I’m on my way to Hausdorff, and from there I’ll take a clipper.”
Fatou nodded. “Do you know how far you’ve climbed?”
“I stopped counting. When I reach Cantor City, it won’t matter how long the journey took.”
“Cantor City,” repeated Fatou. “As I’ve told you before, Cantor City is a dream. The world runs deep, and if Cantor exists it lies above the world entire. If you wish to explore, walk the coastline. There’s no end of places to be found, without moving on to other worlds than this.”
“There has to be an end,” said Pierre. “I’ll find it, if I travel long enough.”
“Perhaps we’re infinitely deep,” said Fatou. “Did you consider that?”
“Julia did, but she never believed it. Julia wouldn’t have left, without something to leave for.”
“You could climb the Set forever, and never reach the surface.”
“Our ancestors mapped us into a structure beyond the reach of entropy,” said Pierre. “Coded us into the substrate of existence. Not even the heat death can touch us. If forever is what it takes, then I’ll climb forever.”
Fatou smiled at him sadly, “Here,” he said, “take this. I have no need of it.”
Pierre accepted the gift, a token for passage. He had accepted one before, and he would accept one again. With that he left Fatou to his orangery. From Shishikura he walked across the desert to Hausdorff. Gothic spires and flying arches rose above an endless knot of slow canals. Crowds flocked and banners billowed in the wind. The crowds, so many, flowed across the bridges of an unreal city. In the distance he could see the Antenna, rising to what seemed like infinity, but he’d climbed that route before and failed.
Instead he booked passage on the next clipper to Feigenbaum, the city that lay across the Cerenean Sea. The clipper was the Lorenz, a proud twin master. Pierre had ridden her before, and he rode her into the coming storm without fear or regret. He wondered if Julia had come this way before him, or whether she’d found another route to Cantor City.
The ocean raced blue beneath eternal orange skies, spiraling against the endless black. Pierre saw worlds within worlds, mirrored in the face of the waters. When the storm came it dashed the Lorenz across the Chasm. The crew were unharmed; death had never been ported over, although loss seemed an inevitable adjunct to humanity in all its forms. Pierre crashed through the waves, refusing the offer of an attractor back to Hausdorff. The crew returned to their origin without him, as they had countless times before.
Pierre struggled beneath the waves, then felt the rising surge and kicked for the surface. The world behind him dwindled. He hoped Fatou would be in the next iteration. There had been a Julia, for the first ten thousand worlds, but she had always moved on before Pierre arrived, following her own path to Cantor. In time, Pierre had reached a world where Julia had never existed, and from then on there was only the trace of her passage. Pierre had yet to catch his own doppel, but he knew the nearest was barely a month ahead, and he could feel his own shadow at his heels.
He followed Julia, and pulled himself across the water. Soon Pierre caught sight of land, and with the last of his strength he struggled ashore. The world he’d left behind was now lost within the endless detail of the new coastline. The beach seemed to be white sand, ground infinitely fine but marked by fading footprints. Pierre had reached the Islands, again.