Neon Downtown Alpha CentauriTRON CumulonimbusFragmented
TRON Cumulonimbus
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Description: The Hénon map parameter space looks a bit like a cumulonimbus cloud as it might appear in the world of "TRON".

Note the pink area at upper right. This is the region where the dynamics can generate strange attractors. It's full of the same swallow-tail forms also found in forced-logistic parameter maps (and these also show up in parameter maps of Volterra-Lotka, and probably all parameter maps of systems of two real variables).

The colored "horns" that overlay the main shape mark locations where there are two or more finite attractors. The biggest horn at the bottom produces period-3 attractors in the cyan region. All of the horns, as well as the main shape, show a period doubling cascade as one moves to the right.
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Posted by: pauldelbrot November 10, 2018, 08:06:32 AM

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