Exotica

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Offline pauldelbrot

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« Reply #60 on: November 17, 2019, 08:53:55 AM »
Nice find. What formula? Seems to have at least two critical points, one of multiplicity 3, and the nonescaping material is multiply-connected, so a rational function of degree at least 5?

Image needs AA but otherwise good.

Offline hgjf2

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« Reply #61 on: November 22, 2019, 09:09:43 PM »
On FRACTVIEW the best 2D android fractal generator.
I used formula "mandel((z^3+z^2)/(z-0.04))" is Newton-like Mandelbrot set. I don't know if fc(z)=(z^6+z^4)/(z^2-0.04) . I believe that uses this formula. You can search this model, after type "mandel((z^3+z^2)/(z-0.04))" in "formula" box. Don't forget to disable autocorrect in smart keyboard for avoid annoying capitulises.

Offline pauldelbrot

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« Reply #62 on: November 24, 2019, 06:17:13 AM »
A Strange Wind Blows

Volterra-Lotka parameter space, multisampling the dynamic space for each point. Coloring combines smooth traps with a radius-3 disk about 1,1 in the dynamic plane and velocity-over-magnitude, which averages |z - zold|/|z| over the orbit's 2nd and subsequent points.

Offline pauldelbrot

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« Reply #63 on: December 07, 2019, 05:47:21 PM »
Exotic Jellyfish

Or maybe an anemone. A Volterra-Lotka Julia with some complex blend of colorings applied.

Offline pauldelbrot

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« Reply #64 on: December 20, 2019, 03:38:10 PM »
Speed

The little "dart" in the Volterra-Lotka parameter space. The bulk of it corresponds to period-2 attractors, but the "whoosh streaks" to the left produce other periods and limit circles, the latter occurring as pairs. Strange attractors may also occur, but the regions outside of the "dart" lack finite attractors entirely. The Julia sets from here look rather different than from the more "classic" Volterra-Lotka ones and can be exceptionally beautiful. One, featuring a limit-circle-pair-just-going-strange, will be forthcoming here under the title "neon blue".

Offline pauldelbrot

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« Reply #65 on: January 02, 2020, 01:28:58 PM »
Sign Above the Chaos Club

A strange attractor from the Hénon map, but the parameters are a bit different from those of the classic Hénon attractor. The shape around the attractor is its basin of attraction; points outside of this go to infinity.

Offline pauldelbrot

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« Reply #66 on: January 14, 2020, 03:40:45 PM »
Serrations

A shallow magnification of the Volterra-Lotka parameter object, showing several of the serrations on its border. The color scheme is simple: blue = periodic, red = limit circle, yellow = strange attractor, black = no finite attractor.