A Strange Wind BlowsCherry TaffyEnigma Orchid
Cherry Taffy
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Description: A Hénon map Julia fractal. There are three discrete-cycle attractors of periods 2 (red basin), 6 (magenta basin), and 16 (blue basin). Note that unlike the one-complex-variable case, where every point bordering two basins borders them all, here in this two-real-variable system we have points on the red/pink border that have neighborhoods containing no blue. The converse doesn't apply: every neighborhood of a blue point that contains red or pink contains all three colors.

Tan points are escaping, and these also break the complex-map rule: whereas the border of the tan region does have all three other basins come arbitrarily close to any point, there is no tan in the interior of the fractal, so red/pink and red/pink/blue border points in the interior of the trapped-points region do not also border tan.
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Posted by: pauldelbrot November 10, 2019, 03:45:16 PM

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