Attractors

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

clifford 1 | Attractors
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

gingerbread man 1 | Attractors

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

gumowski_mira

The strange attractor of Gumowski-Mira.

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

gumowski mira 1 | Attractors

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

henon 1 | Attractors
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

hopalong 1 | Attractors
hopalong 2 | Attractors
ParameterDescription
randomSetting random changes the other parameters to random values (the values will be the same for any value of random)
a – cVariables that define the attractor
startx, 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

lorenz 1 | Attractors

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-mapshttps://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

macmillan 1 | Attractors
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

pdj 1 | Attractors
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

sattractor 1 | Attractors
sattractor 2 | Attractors
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

svensson 1 | Attractors
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

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

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

Info


This information has been created by Rick Sidwell as a guide to the more popular variations used in fractal flames. Not all of the variations are included with JWildfire, but a great many are, so it is worthwhile learning about them here.

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