Attractors


These variations use the formulas for strange attractors. They are mostly normal variations, not blurs, and will produce the actual attractor when used on a single transform by themselves with no affine transforms, as is done with all of the examples shown here. But their use is, of course, not restricted to this. The parameters mostly define the attractor and have no specific meaning.


clifford_js

Strange attractor attributed to Cliff Pickover.

Type: 2D
Author: Jesus Sosa
Date: 4 Nov 2017

Attractors Group Variation clifford
ParameterDescription
a – dVariables that define the attractor

http://paulbourke.net/fractals/clifford/


gingerbread_man

An attractor that resembles a gingerbread man.

Type: 2D Blur
Author: Jesus Sosa
Date: 7 May 2020

Attractors Group Variation gingerbread man

https://mathworld.wolfram.com/GingerbreadmanMap.html


gumowski_mira

The strange attractor of Gumowski-Mira.

Type: 2D Blur
Author: Jesus Sosa
Date: 7 May 2020

Attractors Group Variation gumowski mira

https://www.openprocessing.org/sketch/195425/
https://demonstrations.wolfram.com/StrangeAttractorOfGumowskiMira/


henon

Strange attractor discovered by Michel Hénon.

Type: 2D
Author: Chris Johns (TyrantWave)
Date: 6 Jun 2009

Attractors Group Variation henon
ParameterDescription
a – cVariables that define the attractor; set c to 1 for the classic Hénon map

https://www.deviantart.com/tyrantwave/art/Henon-and-Lozi-Apo-Plugins-125039554
https://mathworld.wolfram.com/HenonMap.html
https://en.wikipedia.org/wiki/H%C3%A9non_map


hopalong

Hopalong attractor, also known as the Martin map.

Type: 2D Blur
Author: Jesus Sosa
Date: 7 May 2020

Attractors Group Variation hopalong
Attractors Group Variation hopalong
ParameterDescriptionrandomSetting random changes the other parameters to random values (the values will be the same for any value of random)a – cVariables that define the attractorstartx, startyStarting values for plotting the attractor

http://www.fraktalwelt.de/myhome/simpiter2.html
https://www.youtube.com/watch?v=JhHugpABjDo


lorenz_js

Strange attractor first studied by Edward Lorenz.

Type: 3D Direct Color
Author: Jesus Sosa
Date: 12 Dec 2017

Attractors Group Variation lorenz

Lorenz uses Euler’s method to solve the Lorenz system of ordinary differential equations. Coloring is based on the resulting x and y values.

ParameterDescription
a – cVariables that define the attractor; a is sometimes known as the Prandtl number and b the Rayleigh number
hStep size for the Euler approximation
centerx, centeryOffset for direct coloring
scaleScale for direct coloring

http://paulbourke.net/fractals/lorenz/

https://en.wikipedia.org/wiki/Lorenz_system

https://en.wikipedia.org/wiki/Euler_method


lozi

Strange attractor discovered by René Lozi.

Type: 2D
Author: Chris Johns (TyrantWave)
Date: 6 Jun 2009

http://padyn.wikidot.com/lozi-maps

https://mathworld.wolfram.com/LoziMap.html

https://www.deviantart.com/tyrantwa

https://www.deviantart.com/tyrantwave/art/Henon-and-Lozi-Apo-Plugins-125039554

http://padyn.wikidot.com/lozi-maps

https://mathworld.wolfram.com/LoziMap.html

ParameterDescription
a – cVariables that define the attractor; set c to 1 for the classic Lozi map

macmillan

Perturbed McMillan map (studied by Edwin McMillan)

Type: 2D blur
Author: Jesus Sosa
Date: 29 Mar 2018

Attractors Group Variation macmillan
ParameterDescription
a – bVariables that define the attractor
startx, startyStarting point

http://www.3d-meier.de/tut19/Seite158.html


pdj

Peter de Jong attractor

Type: 2D
Author: Scott Draves
Date: Sept 2003

Attractors Group Variation pdj
ParameterDescription
a – dVariables that define the attractor

http://paulbourke.net/fractals/peterdejong/

https://www.algosome.com/articles/strange-attractors-de-jong.html


sattractor_js

A strange attractor attributed to Roger Bagula.

Type: 2D
Author: Jesus Sosa
Date: 21 Dec 2017

Attractors Group Variation sattractor
Attractors Group Variation sattractor 2
ParameterDescription
mSymmetry of the attractor, integer between 2 and 12

http://paulbourke.net/fractals/henonattractor/


svensson_js

Johnny Svensson attractor, based on the Peter de Jong attractor.

Type: 2D
Author: Jesus Sosa
Date: 12 Dec 2017

Attractors Group Variation svensson
ParameterDescription
a – dVariables that define the attractor

http://paulbourke.net/fractals/peterdejong/


threeply

A strange attractor named Three Ply

Type: 2D Blur
Author: Jesus Sosa
Date: 7 May 2020

Attractors Group Variation threeply 1
Attractors Group Variation threeply 2
ParameterDescription
a – cVariables that define the attractor

http://www.jamesh.id.au/fractals/orbit/threeply.html



This information has all been created by Rick Sidwell as a guide to the more popular variations used in fractal flames, and very generously allowed me to reproduce it here. Not all of the variations are included with JWildfire, but a great many are, so it is worthwhile learning about them.
Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.


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