# Julia

Variations based on polynomial Julia sets. For escape time fractals, the formula is z → z^n + c. For flames, the mapping is reversed and the “+ c” part is done by the affine transform, so these variations basically take the root of the input taken as a complex number, returning one of the results at random.

Based on complex numbers, the Julia transform is two dimensional by nature. Some 3D Julia variants have been written, but the 3D transformation is not related to the basic Julia operation.

Several other variations have incorporated the functionality of julian, including cpow, wavesn, and xtrb.

## eJulia

Polynomial Julia sets in elliptic coordinates

Type: 2D
Author: Michael Faber
Date: 24 Jun 2012

Parameter Description
power The power for the polynomial; 2 for quadratic. Must be an integer. Negative values are allowed and return the reciprocal.

## julia

Classic quadratic Julia set (obsolete; use julian with power=2).

Type: 2D
Author: Scott Draves
Date: 1 Feb 2004

The original Julia implementation, it has a bug: it swaps x and y. This was never fixed because doing so would break earlier flames. The workaround is to use julian with power set to 2.

## julia3D

Classic polynomial Julia set with 3D extrusion.

Type: 3D
Author: Joel Faber

Parameter Description
power The power for the polynomial; 2 for quadratic. Must be an integer. Negative values are allowed and return the reciprocal.

## julia3D_fl

“Fluid” version of julia3D; allows fractional values for power.

Type: 3D
Author: Fred E (morphapoph)
Date: 8 Sep 2010

Parameter Description
power The power for the polynomial; 2 for quadratic. May be fractional. Negative values are allowed and return the reciprocal.

https://www.deviantart.com/morphapoph/art/Apo-Anim-friendly-Plugins-178559281

## julia3Dq

Julia set using a rational power with 3D extrusion. Also post_julia3Dq.

Type: 3D
Author: Peter Sdobnov (Zueuk)
Date: 2 Dec 2012

Parameter Description
power The numerator of the polynomial power. Must be an integer. Negative values are allowed and return the reciprocal.
divisor The denominator of the polynomial power.

https://www.deviantart.com/zueuk/art/juliaq-Apophysis-plugins-340813357

## julia3Dz

Classic polynomial Julia set with 3D extrusion.

Type: 3D

Parameter Description
power The power for the polynomial; 2 for quadratic. Must be an integer. Negative values are allowed and return the reciprocal.

## julia3Dz_fl

“Fluid” version of julia3Dz; allows fractional values for power

Type: 3D
Author: Fred E (morphapoph)
Date: 8 Sep 2010

Parameter Description
power The power for the polynomial; 2 for quadratic. May be fractional. Negative values are allowed and return the reciprocal.

https://www.deviantart.com/morphapoph/art/Apo-Anim-friendly-Plugins-178559281

## juliac

Julia set using a complex power.

Type: 2D
Author: David Young (Sc0t0ma)
Date: 9 Sep 2008

Parameter Description
re The real part of the complex power. Negative values are allowed and return the reciprocal.
im The imaginary part of the complex power.
dist Distortion factor; increase to stretch the result and help fill in the hole normally left in the middle. Negative values do an inversion (aka spherical).

https://www.deviantart.com/sc0t0ma/art/Juliac-97512904

## juliacomplex

Julia set using a complex power.

Type: 2D
Author: Luca G (dark-beam)
Date: 21 Nov 2011

Parameter Description
Re_p The real part of the complex power. Negative values are allowed and return the reciprocal.
Im_p The imaginary part of the complex power.
dist Distortion factor; increase to stretch the result and help fill in the hole normally left in the middle. Negative values do an inversion (aka spherical).
logadd An addition to the imaginary part; changes the shape of the “blades”

https://www.deviantart.com/dark-beam/art/Juliacomplex-apoplugin-270181347

## julian

Classic polynomial Julia set

Type: 2D
Author: Scott Draves
Date: 15 Apr 2006

Often referenced as “juliaN” to emphasize it is julia with an “N” parameter, but the variation name is all lower case.

Parameter Description
power The power for the polynomial; 2 for quadratic. Must be an integer. Negative values are allowed and return the reciprocal.
dist Distortion factor; increase to stretch the result and help fill in the hole normally left in the middle. Negative values do an inversion (aka spherical).

## julian_fl

“Fluid” version of julian; allows fractional values for power

Type: 3D
Author: Fred E (morphapoph)
Date: 8 Sep 2010

Parameter Description
power The power for the polynomial; 2 for quadratic. May be fractional. Negative values are allowed and return the reciprocal.
dist Distortion factor; increase to stretch the result and help fill in the hole normally left in the middle. Negative values do an inversion (aka spherical).

https://www.deviantart.com/morphapoph/art/Apo-Anim-friendly-Plugins-178559281

## julian2

Julian with an integrated affine transform. Also post_julian2.

Type: 2D
Author: Georg Kiehne (xyrus02)
Date: 11 Sep 2009

Parameter Description
power The power for the polynomial; 2 for quadratic. Must be an integer. Negative values are allowed and return the reciprocal.
dist Distortion factor; increase to stretch the result and help fill in the hole normally left in the middle. Negative values do an inversion (aka spherical).
a – f Affine coefficients: (x,y) → (ax+by+e, cx+dy+f)

## julian2dc

Julian2 with direct color.

Type: 2D Direct Color
Author: Georg Kiehne (xyrus02)
Date: 16 Dec 2010

Parameter Description
power The power for the polynomial; 2 for quadratic. Must be an integer. Negative values are allowed and return the reciprocal.
dist Distortion factor; increase to stretch the result and help fill in the hole normally left in the middle. Negative values do an inversion (aka spherical).
col Controls direct color; 0 for radial, 1 for circles, others for spiral
a – f Affine coefficients: (x,y) → (ax+by+e, cx+dy+f)

http://xyrus-worx.org/Content/apophysis.directcolor.php (Defunct)
https://sourceforge.net/p/apo-plugins/code/HEAD/tree/personal/georgkiehne/julian2dc.c

## julian3Dx

Julian2 with 3D wave effect

Type: 3D
Author: Georg Kiehne (xyrus02)
Date: 21 May 2014

Parameter Description
power The power for the polynomial; 2 for quadratic. Must be an integer. Negative values are allowed and return the reciprocal.
dist Distortion factor; increase to stretch the result and help fill in the hole normally left in the middle. Negative values do an inversion (aka spherical).
a – f Affine coefficients: (x,y) → (ax+by+e, cx+dy+f)

## juliaNab

Variant of julian with different parameters.

Type: 2D
Author: Ffey
Date: 2 Aug 2011

Parameter Description
n The power for the polynomial; same as julian parameter power
a Distortion factor; same as julian parameter dist
b Added to x and y; shifts result diagonally
separ Power for x; integers work best

## juliaq

Julia set using a rational power. Also post_juliaq.

Type: 2D
Author: Peter Sdobnov (Zueuk)
Date: 2 Dec 2012

Parameter Description
power The numerator of the polynomial power. Must be an integer. Negative values are allowed and return the reciprocal.
divisor The denominator of the polynomial power.

https://www.deviantart.com/zueuk/art/juliaq-Apophysis-plugins-340813357

## npolar

Mashup of julian and polar2.

Type: 2D
Author: Georg Kiehne (xyrus02)
Date: 8 Apr 2010

Parameter Description
parity When odd, parity is a scale factor for julian; no polar2 is done.
When even, npolar first does polar2, then julian, then polar2 with x and y reversed; the value of parity is not used.
n The power for the polynomial; same as julian parameter power

## phoenix_julia

Julian with extra distortion parameters.

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

Parameter Description
power The power for the polynomial; 2 for quadratic. Non-integer values are allowed. Negative values are allowed and return the reciprocal.
dist Distortion factor; increase to stretch the result and help fill in the hole normally left in the middle. Negative values do an inversion (aka spherical).
x_distort Distortion factor for x.
y_distort Distortion factor for y.

https://www.deviantart.com/tyrantwave/art/PhoenixJulia-Apophysis-Plugin-121246658

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.

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