Mandelbrot FoamTaffy
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Description: The Hénon attractor is produced by a mapping of two real variables that has two real parameters. This is a Julia set, but with different parameter values than for the "classic" Hénon attractor. The parameter change has broken the strange attractor in two (dark squiggles on yellow), and caused the appearance of a second, non-strange attractor, a cycle of seven points (darkest regions in biggest brown patches). Their attracting basins (yellow and brown areas, respectively) resemble two differently colored toffees swirled together. Green points escape to infinity. The Julia set, unlike in the one-complex-variable case, is not identical to the border of each attracting basin. There are no green areas dotted along the borders between brown and yellow areas. Much of the Julia set does not border A(∞), though, interestingly, all of the border of A(∞) seems to be approached in the limit by both of the other attracting basins, and by the border between them.

A(∞) is colored by smoothed iterations. Each of the other basins is colored by the squared distance to the nearest point of that basin's attractor. All gradients shade to black for zero iterations/distance.
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Filesize: 922.98kB
Height: 1536 Width: 2048
Posted by: pauldelbrot April 26, 2018, 06:16:10 AM

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