A whole geometric universe fits into seven characters: z → z² + c. For each point c on the complex plane, the sequence starting at 0 either loiters near the origin forever or crosses radius 2 and flies off to infinity, and those two fates alone paint the Mandelbrot set. Its boundary is infinitely long while its area stays finite: the deeper the zoom into Seahorse Valley near −0.745 + 0.1135i, the more never-ending filigree appears, while near −1.7687 a tiny copy of the entire set hangs in the void.
A whole geometric universe fits into seven characters: z → z² + c. For each point c on the complex plane, the sequence starting at 0 either loiters near the origin forever or crosses radius 2 and flies off to infinity, and those two fates alone paint the Mandelbrot set. Its boundary is infinitely long while its area stays finite: the deeper the zoom into Seahorse Valley near −0.745 + 0.1135i, the more never-ending filigree appears, while near −1.7687 a tiny copy of the entire set hangs in the void.
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