Mandelbrot set 

fractal-like set that plays a significant role in chaos research Gigapixel image of the Mandelbrot set (allows deepest possible zoom in PNGs as of 2021)  image   video
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Instance of	fractal (boundary) subset (set of complex numbers) mathematical concept
Part of	set of complex numbers
Named after	Benoit Mandelbrot
Based on	Julia set
Authority file  Q257 Reasonator Scholia Wikidocumentaries KML file Search depicted

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  Benoît Mandelbrot and the set bearing his name

General

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  Hi-resolution Mandelbrot set with axes
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  Mandelbrot set and periodicities of orbits
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  Mandelbrot set and colorcoded periodicities of orbits
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  Mandelbrot set with well defined colour stripes
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  Mandelbrot set with irregular colour stripes
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  Mandelbrot set in grayscale
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  Mandelbrot set with smooth color gradient
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  Buddhabrot
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  Mandelbrot zoom
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  Inside colour-mapping, (B&W version).
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  Inside colour-mapping, (colour version).
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  Screenshot von RFL Mandelbrot Set Exploration Tool v0.0.4
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  Visualization of Mandelbrot set in complex plane
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  Command-line depiction of the Mandelbrot set.
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  Yet another image of the Mandelbrot Set.
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  Representation of Inner Structure
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  colors

Structure

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  Boundaries of hyperbolic components of mandelbrot set
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  Lemniscates - boundaries of level sets of escape time
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  Centers of hyperbolic components
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  All boundaries of level sets of escape time up from n=1

Rays

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  External and internal rays, center and root
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  External rays of Misiurewicz point
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  External ray of Misiurewicz point c=-2
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  Uniformization of complement of Mandelbropt set
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  Wakes near the period 1 continent in the Mandelbrot set
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  Wakes along the main antenna in the Mandelbrot set

Fractalizer

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  Example 01
  www.fractalizer.de/en archive copy at the Wayback Machine
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  Example 02
  www.fractalizer.de/en archive copy at the Wayback Machine
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  Example 03
  www.fractalizer.de/en archive copy at the Wayback Machine
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  Example 04
  www.fractalizer.de/en archive copy at the Wayback Machine
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  Example 05
  www.fractalizer.de/en archive copy at the Wayback Machine
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  Example 06
  www.fractalizer.de/en archive copy at the Wayback Machine
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  Example 07
  www.fractalizer.de/en archive copy at the Wayback Machine
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  Example 08
  www.fractalizer.de/en archive copy at the Wayback Machine
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  Example 09
  www.fractalizer.de/en archive copy at the Wayback Machine
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  Example 10
  www.fractalizer.de/en archive copy at the Wayback Machine
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  Example (video) 01
  www.fractalizer.de/en archive copy at the Wayback Machine
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  Example (video) 02
  www.fractalizer.de/en archive copy at the Wayback Machine

Zoom

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  Initial image of a zoom sequence with 14 steps
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  Initial image of a corresponding zoom sequence with frames
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  Zoom step 1 of 14
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  Zoom step 1 of 13
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  Zoom step 2 of 14
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  Zoom step 2 of 13
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  Zoom step 3 of 14
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  Zoom step 3 of 13
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  Zoom step 4 of 14
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  Zoom step 4 of 13
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  Zoom step 5 of 14
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  Zoom step 5 of 13
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  Zoom step 6 of 14
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  Zoom step 6 of 13
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  Zoom step 7 of 14
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  Zoom step 7 of 13
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  Zoom step 8 of 14
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  Zoom step 8 of 13
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  Zoom step 9 of 14
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  Zoom step 9 of 13
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  Zoom step 10 of 14
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  Zoom step 10 of 13
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  Zoom step 11 of 14
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  Zoom step 11 of 13
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  Zoom step 12 of 14
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  Zoom step 12 of 13
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  Zoom step 13 of 14
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  Zoom step 13 of 13
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  Zoom step 14 of 14
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  Mandelbrot (Ausschnitt)
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  Mandelbrot (Ausschnitt)
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• Zooming Movie 03
• Zooming movie 04
• Zooming movie 06
• Zooming movie 15
• High-resolution zoom
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  Featured golden gradient zoom on the Mandelbrot set by more than 31 orders of magnitude.

Iteration

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  At a count of 32, the whole image is black, since it is completely inside the false-negative contour.
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  If we allow 64 iterations, some points are no longer falsely inside the set.
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  At 128 iterations, the image is blobby, but recognizable as a fractal.
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  256
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  At 512, we get a nice image. The black dots up and to the left of each "wart" contain tiny cardioids.
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  1024
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  2048
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  Diminishing returns are quite obvious when we use a million iterations. Even with periodicity checking, this one took 10–15 seconds to generate on an Athlon XP 2000+.
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  Number of iterations changing from 1 to 50.

Art and the Mandelbrot set

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  Calm Mandelbrot, magnified 100,458,337,236 times, 256 iterations
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  Cool Mandelbrot, magnified 248,034,982,258 times, 256 iterations
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  Hot Mandelbrot, magnified 261,880 times, 1024 iterations
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  Galaxy of Galaxies
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  Rendered with a scenery generator
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• Spiral, Color cycling animation
• Spiral, Color cycling animation 2
• Spiral, Color cycling animation 3
• Spiral, Color cycling animation 4
• Spiral, Color cycling animation 5
• Spiral, Color cycling animation 6
• Spiral, Color cycling animation 7
• Spiral, Color cycling animation 8
• Spiral, Color cycling animation 9
• Spiral, Color cycling animation 10
• Spiral, Color cycling animation 11
• Spiral, Color cycling animation 12
• Spiral, Color cycling animation 13
• Spiral, Color cycling animation 14
• Spiral, Color cycling animation 15
• Spiral, Color cycling animation 16
• Spiral, Color cycling animation 17
• Spiral, Color cycling animation 18

Universality of Mandelbrot set

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  Mandelbrot sets occurring in the analysis of Newton's method
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  Mandelbrot set occurring in the analysis of Newton's method (detail)
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  Mandelbrot set occurring in the analysis of Newton's method (detail)
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  Mandelbrot set occurring in a model of phase transitions (detail)
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  Mandebrot set embedded in cos(z)+c.
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  Mandebrot set embedded in gaussian exp(-z^2)+c.

Miscellaneous

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  Comparing functions, Mandel/Bifurcation.
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  Periodic cycles in the Mandelbrot set
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  Mandelbrot, plane: 1/lambda
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  Relation between Mandelbrot set and en:logistic map
• Multibrot sets
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  Map of Julia sets showing the resemblance with the Mandelbrot set
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  Mandelbulber v2.23
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  High-resolution Buddhabrot rendering of the Mandelbrot set

First steps in Mandelbrot set

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  1.step of Ms
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  2.step of Ms
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  3.step of Ms
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  4.step of Ms
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  5.step of Ms
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  9.step of Ms
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  30.step of Ms
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  part of 30.step of Ms
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  step 1
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  step 2
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  step 3
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  step 4
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  step 5
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  step 6
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  step 7
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  step 8
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  step 9
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  step 10
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  step 11
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  step 12
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  step 13
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  step 14
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  step 15
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  step 16
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  step 17
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  step 18
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  step 19
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  step 20