### Exotica

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• 3f
• Posts: 1986

#### Re: Exotica

« 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.

#### hgjf2

• Fractal Friar
• Posts: 117

#### Re: Exotica

« 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.

• 3f
• Posts: 1986

#### Re: Exotica

« 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.

• 3f
• Posts: 1986

#### Re: Exotica

« 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.

• 3f
• Posts: 1986

#### Re: Exotica

« 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".

• 3f
• Posts: 1986

#### Re: Exotica

« 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.

• 3f
• Posts: 1986

#### Re: Exotica

« 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.

• 3f
• Posts: 1986

#### Re: Exotica

« Reply #67 on: January 26, 2020, 10:39:28 AM »
Enigma Fish

• 3f
• Posts: 1986

#### Re: Exotica

« Reply #68 on: February 06, 2020, 03:42:08 PM »
Order and Chaos

A Volterra-Lotka Julia set featuring both order (purple, basin of a cyclic attractor, dark dots) and chaos (orange-brown, basin of a strange attractor, bright yellow tangled threads). Note that the periodic attractor has a period up in the 30s or so while the strange attractor is in segments, 11 of them, that themselves are cyclically permuted by the iteration.

• 3f
• Posts: 1986

#### Re: Exotica

« Reply #69 on: February 15, 2020, 05:23:41 PM »
VL Julia Mosaic 3

Volterra-Lotka Julia mosaic showing one of the parameter object's serrations. Attractors are plotted in each Julia set. Grey = periodic cycle finite attractor, yellow = limit circle, red = strange, blue = escapes.

• 3f
• Posts: 1986

#### Re: Exotica

« Reply #70 on: February 25, 2020, 09:33:46 AM »
Stirring Coffee

• 3f
• Posts: 1986

#### Re: Exotica

« Reply #71 on: March 10, 2020, 01:28:28 PM »
Raspberry and Toffee

A Hénon map Julia set. There are three attracting basins: infinity (green), a 2-cycle (yellow), and a 3-cycle (pink). The white bands separate the components of the 2-cycle's basin: in the map that iterates the Hénon map twice at once, this becomes two separate fixed points and the white bands border their respective basins. In systems of one complex variable, there would have to be green intruding between pink and yellow, and both pink and green intruding along those white bands; here, in a system of two real variables, that constraint does not exist. Instead there again seems to be a hierarchy of basins, where all others accumulate to the border with escaping points, and both phases of the yellow basin accumulate to the border of the 3-cycle's basin, but nothing else accumulates to the border between the two yellow phases.

• 3f
• Posts: 1986

#### Re: Exotica

« Reply #72 on: March 21, 2020, 05:20:19 PM »
Enigma Grass

#### Dinkydau

• Fractal Furball
• Posts: 271

#### Re: Exotica

« Reply #73 on: March 21, 2020, 10:35:34 PM »
nice

• 3f
• Posts: 1986

#### Re: Exotica

« Reply #74 on: March 21, 2020, 10:44:49 PM »
Thanks!