Cpow – Complex Power

Home » Variation Types » Cpow - Complex Power

Cpow – Complex Power

Treats 2D points as complex numbers and raises them to a complex power that can be specified in various ways.

cpow

Raise input point to a complex power specified by its real and imaginary parts.

Type: 2D
Author: Joel Faber
Date: 10 Aug 2008

ParameterDescription
rReal part of the power
iImaginary part of the power
powerDivides the complex power by this amount. This also shrinks the result, which is then replicated radially this many times to fill the vacated space (aka julian).

The plugins restrict power to be an integer; JWildfire does not.

https://sourceforge.net/projects/apo-plugins/files/apo-plugins/80810/

http://guagapunyaimel.deviantart.com/art/cpow-ring2-tutorial-192002748

cpow2

Raise input point to a complex power specified in polar coordinates.

Type: 2D
Author: Peter Sdobnov (Zueuk)
Date: 13 Mar 2009

ParameterDescription
rMagnitude of the power; normally positive
aAngle of the power between -2 and 2 (neither radians nor degrees)
divisorDivides the complex power by this amount. This also shrinks the result, which is then replicated radially this many times to fill the vacated space (aka julian).
rangeControls the number of values beyond the principal value that are included; must be an integer at least 1.

http://phoenixkeyblack.deviantart.com/art/cpow2-141045125

http://sourceforge.net/p/apo-plugins/code/HEAD/tree/personal/petersdobnov/

cpow3

Raise input point to a complex power to produce a spiral

Type: 2D
Author: Anton Liasotskiy (zy0rg)
Date: March 2013

This variation was never released by its author, but has been frequently shared in fractal chat rooms and forums. It is included in the Essential Plugin Pack at http://bezo97.tk/plugins.html, and has been implemented in JWildfire starting with version 3.21.

ParameterDescription
rRotation; the fraction of a circle that 360° is mapped to, so 1 means the output spiral matches the shape of the input and smaller values wind the spiral more tightly.
dDistance; the proportional distance between successive rotations of the spiral. If the input is a shape with a hole that takes 75% of the shape, setting d to 0.75 will make the successive rotations fit in the hole. The direction of the spiral is reversed when d is negative.
divisorDivides the complex power by this amount. This also shrinks the result, which is then replicated radially this many times to fill the vacated space (aka julian).
spreadControls the number of values beyond the principal value that are included. The default value of 1 will dynamically adjust the number of values used based on the r and d values, and will normally not need to be increased. However it may be decreased to reduce the number of values down to a minimum of 0, which includes 1 value on each side of the principal value.

https://fractal2cry.deviantart.com/art/Cpow3-fractal-360743627

https://pillemaster.deviantart.com/art/Cauliflower-374228018

https://tatasz.deviantart.com/art/Cpow3-without-overlaps-710419456

cpow3_wf

Attempt to port cpow2 to JWildfire that “by happy accident became something else”.

Type: 2D
Author: Gregg Helt (cozyg)
Date: 11 Mar 2015

This variation is the result of a serendipitous mistake the author made while attempting to implement cpow2 in JWildfire. He liked the results, so released this variation. It was originally added to JWildfire with the name “cpow3”, but it was renamed to “cpow3_wf” when the above cpow3 was added in JWildfire version 3.21.

https://jwildfire.overwhale.com/forum/viewtopic.php?f=23&t=1743

droste

Implements Escher’s map using logarithms; same effect as escher.

Type: 2D
Author: Joel Faber (unreleased)

Droste was “test code that [the author] forgot to delete” when he first released the plugin package containing escher. It was deleted from later versions, but still made its way into plugin collections. It does the same thing as escher

ParameterDescription
r1, r2The ratio r2/r1 determines the power

http://www.josleys.com/article_show.php?id=82

http://www.deviantart.com/art/BD-s-2-New-Scripts-80636384

http://www.deviantart.com/art/BD-s-Droste-Plastic-script-76392380

escher

Implements Escher’s Map by treating each point of the flame as a complex number and raising it to a power determined by the variable beta.

Type: 2D
Author: Joel Faber
Date: 21 Oct 2007

ParameterDescription
betaControls the power. The effective range is -π to π, though values near the extremes are not very useful.

Setting beta to 0 makes escher behave like linear.

https://sourceforge.net/projects/apo-plugins/files/apo-plugins/80810/

http://mathworld.wolfram.com/EschersMap.html

Leave a Comment



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.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.