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.
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. |
Apophysis plugin
eJulia tutorial
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.
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. |
"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. |
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. |
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. |
"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. |
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). |
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" |
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 variation information at JWildfire Sanctuary
Julians Fractal Styles article
Julia, Julian and Julianscopes tutorial
Julia Uncovered v.2.2
Julian Tutorial log (Transcript of a chat session)
Spiked 3D Julian tutorial
Julian Rings tutorial (Wayback Machine)
LazyJulian tutorial
The Rings2 and Julian Guide
Wire and Tube Fractals tutorial
Apophysis Base Forms Pack
Fractal Stars tutorial
How Julia transforms work article
Simple 3D Julian and DOF tutorial
"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). |
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) |
Archive of Apophysis plugin page (Wayback Machine)
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) |
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) |
Archive of Apophysis plugin (Wayback Machine)
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 |
Archive of Apophysis plugin (Wayback Machine)
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. |
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 |
Archive of Apophysis plugin (Wayback Machine)
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. |