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
| Parameter | Description |
|---|---|
| a – d | Variables 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
https://mathworld.wolfram.com/GingerbreadmanMap.html
gumowski_mira
The strange attractor of Gumowski-Mira.
Type: 2D Blur
Author: Jesus Sosa
Date: 7 May 2020
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
| Parameter | Description |
|---|---|
| a – c | Variables 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
| 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
Lorenz uses Euler’s method to solve the Lorenz system of ordinary differential equations. Coloring is based on the resulting x and y values.
| Parameter | Description |
|---|---|
| a – c | Variables that define the attractor; a is sometimes known as the Prandtl number and b the Rayleigh number |
| h | Step size for the Euler approximation |
| centerx, centery | Offset for direct coloring |
| scale | Scale 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
| Parameter | Description |
|---|---|
| a – c | Variables 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
| Parameter | Description |
|---|---|
| a – b | Variables that define the attractor |
| startx, starty | Starting point |
http://www.3d-meier.de/tut19/Seite158.html
pdj
Peter de Jong attractor
Type: 2D
Author: Scott Draves
Date: Sept 2003
| Parameter | Description |
|---|---|
| a – d | Variables 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
| Parameter | Description |
|---|---|
| m | Symmetry 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
| Parameter | Description |
|---|---|
| a – d | Variables 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
| Parameter | Description |
|---|---|
| a – c | Variables that define the attractor |
http://www.jamesh.id.au/fractals/orbit/threeply.html
