Other Polynomial and Rational Maps

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Offline pauldelbrot

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« Reply #45 on: June 18, 2019, 04:27:52 PM »
Herman Ring

A Herman Ring. Found in the Supernova formula and rendered using DE. The linked black rings are the Herman ring together with its preimages. White is the Julia set. The exterior black region and all simply-connected black regions are parts of A(∞) and A(0). 0 is in the interior of, and near the center of, the lower of the largest two simply-connected black regions.

Offline pauldelbrot

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« Reply #46 on: June 27, 2019, 07:37:23 PM »
Bugs

These bugs' bodies are minibrots on the antenna of z12 + c.

Offline pauldelbrot

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« Reply #47 on: July 08, 2019, 06:49:15 AM »
Metal

Fitted together strangely, along a fractal curve.

Matchmaker, with attracting fixed point.

Offline pauldelbrot

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« Reply #48 on: July 17, 2019, 03:37:02 AM »
Geothermal Pools

Tinted by strange bacteria.

Supernova, zoomed in a seahorse-spirally area. Yellow and blue areas go to distinct attractors, but both colors shift to others at higher iterations ...

Offline pauldelbrot

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« Reply #49 on: July 28, 2019, 05:32:58 AM »
The Breakdown of the Bicameral Mind

Supernova parameter space

Offline pauldelbrot

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« Reply #50 on: August 10, 2019, 02:35:02 AM »
Autumnal

Offline pauldelbrot

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« Reply #51 on: August 18, 2019, 04:08:58 PM »
Hooked

Triskelion Julia set

Offline pauldelbrot

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« Reply #52 on: September 01, 2019, 04:54:57 PM »
Whirlpools IV

A triple matchmaker Julia set bounding the basins of two stable attracting cycles.

Offline pauldelbrot

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« Reply #53 on: September 11, 2019, 07:03:49 AM »
Supernova Double Spiral

Offline pauldelbrot

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« Reply #54 on: September 23, 2019, 05:50:06 PM »
Autumn Twist

Offline hgjf2

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« Reply #55 on: September 27, 2019, 08:22:55 AM »
Superb polynomial compositions!
 :thumbs_up_by_craig_m: Paul's collection

Offline pauldelbrot

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« Reply #56 on: September 27, 2019, 09:00:18 AM »
Thanks!

Offline pauldelbrot

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« Reply #57 on: October 05, 2019, 09:39:39 AM »
Nonelastic Polymer

Paramater space region of triple matchmaker, blending various coloring mode/critical orbit combinations.

Offline pauldelbrot

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« Reply #58 on: October 15, 2019, 07:28:02 PM »
Mandibles

Supernova parameter space. Sometimes the Herman mirrors fork, always into three tines and always with a right-angled intersection in the middle.

Offline pauldelbrot

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« Reply #59 on: October 28, 2019, 09:44:41 AM »
Ghost Bulb

This spooky image comes from Supernova's parameter space. One of the other critical points has a bulb here. It casts a "shadow" onto this plane in the form of dark purplish filled-in-Julia shapes inside of its circular borders.