Exotica

  • 89 Replies
  • 4058 Views

0 Members and 1 Guest are viewing this topic.

Offline pauldelbrot

  • *
  • 3f
  • ******
  • Posts: 2192
« Reply #75 on: April 02, 2020, 10:49:23 PM »
Deepfish

Hénon map parameter space, near the upper end of the "chaos beach". There are leaping fish like things here within which there are finite attractors, surrounded by a region of parameters where only infinite attracts.

Offline pauldelbrot

  • *
  • 3f
  • ******
  • Posts: 2192
« Reply #76 on: April 12, 2020, 05:02:01 PM »
Chain in Fog

Multisampled parameter space image of Enigma. This blurs the seahorsey dendrites and other such details, but makes the regions that have finite attractors (the Mandelbrot set analogue) fully visible -- and it seems to possess Herman mirrors.

Offline pauldelbrot

  • *
  • 3f
  • ******
  • Posts: 2192
« Reply #77 on: April 22, 2020, 07:18:32 PM »
Enigma Black Dahlia

Offline pauldelbrot

  • *
  • 3f
  • ******
  • Posts: 2192
« Reply #78 on: May 03, 2020, 06:47:05 PM »
Ice Storm

A Volterra-Lotka parameter space visualization.

Offline pauldelbrot

  • *
  • 3f
  • ******
  • Posts: 2192
« Reply #79 on: May 14, 2020, 10:53:08 PM »
Omnibrot DLD

Unzoomed omnibrot with the Discrete Langrangian Descriptor coloring method, studying the singular orbit.

Though it's included here for having a transcendental function in the formula, it actually behaves in many respects like a rational map, but gives "zed to the infinity" minibrots on the singular orbit.

Offline pauldelbrot

  • *
  • 3f
  • ******
  • Posts: 2192
« Reply #80 on: May 28, 2020, 11:04:36 AM »
Organoform

Forced logistic with sequence BABBA; multisampled for starting value.

Offline pauldelbrot

  • *
  • 3f
  • ******
  • Posts: 2192
« Reply #81 on: June 09, 2020, 03:31:16 PM »
Ice Peak

Ibiza parameter space slice, multisampled.

Offline pauldelbrot

  • *
  • 3f
  • ******
  • Posts: 2192
« Reply #82 on: June 21, 2020, 01:37:06 AM »
Rainbow Ribbon

A discrete Volterra-Lotka strange attractor.

Offline pauldelbrot

  • *
  • 3f
  • ******
  • Posts: 2192
« Reply #83 on: July 04, 2020, 10:20:25 PM »
Stirred

Discrete Volterra-Lotka Julia set with one finite attractor, a discrete cycle with a fragmentary basin. This is the sort of thing that happens for parameters in one of the narrow protrusions past the main bulk of the parameter object.

Offline pauldelbrot

  • *
  • 3f
  • ******
  • Posts: 2192
« Reply #84 on: July 16, 2020, 08:07:14 PM »
Enigma Jellyfish

Enigma parameter space slice

Offline pauldelbrot

  • *
  • 3f
  • ******
  • Posts: 2192
« Reply #85 on: August 05, 2020, 12:40:00 AM »
Whorls

Offline pauldelbrot

  • *
  • 3f
  • ******
  • Posts: 2192
« Reply #86 on: August 16, 2020, 02:44:48 PM »
Doomed Binary

Offline pauldelbrot

  • *
  • 3f
  • ******
  • Posts: 2192
« Reply #87 on: August 26, 2020, 12:46:32 AM »
Flock in Storm

This discrete Volterra-Lotka parameter space image looks like a flock of birds caught in bad weather.

Mathematically: the blue in top right lacks finite attractors, or their basins are thin and wispy; the grey "slats" at left are regions with limit circle attractors, with the narrower bands between the slats producing discrete cyclic attractors; the swirling grey in most of the rest of the image produces strange attractors; and the pale "birds", their shapes familiar from the forced logistic map and some other two-real-parameter fractals, are islands of stability with, again, discrete cycles.

Offline pauldelbrot

  • *
  • 3f
  • ******
  • Posts: 2192
« Reply #88 on: September 07, 2020, 10:28:48 PM »
Hollow Core

Mandelbrot Foam

Offline pauldelbrot

  • *
  • 3f
  • ******
  • Posts: 2192
« Reply #89 on: September 20, 2020, 03:42:27 PM »
When Strangeness Reaches Out

Hénon map parameter space near the edge of the strange attractor region "Chaos Beach". The dark shapes are islands of periodicity.

Color gradient is determined by a combination of curvature and "wiggliness" of the orbit. (A sine wave would have curvature zero, from averaging out to a straight line due to alternately turning both ways, but would be quite wiggly.)