Infinitely FoldedAt the Mountains of MadnessCosmic Knot
At the Mountains of Madness
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Description: What seems from a distance to be a mountain in a range seems, on closer inspection, to dissolve into mist and cloud not quite concealing shadowy nameless beasts ...

Formula: Ibiza parameter space. Ibiza is:

\( x_{n+1} = 1 - ax_n^2 + y_n \)
\( y_{n+1} = bx_n y_n + cy_n^3 - 1 \)

which is a two-real-variable system with three parameters. The image is in the a/b plane with c fixed at 0.1. Coloring is 2D combining average atan x over the attractor with ln(average of 1/|P|2 over the orbit) where P is the orbit point and |P| is the usual Euclidean norm. It is possible to see the "swallowtails" and other related structures here and there.
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Posted by: pauldelbrot June 04, 2019, 10:46:45 PM

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