HomeVariation TypesPolar Shapes

Polar Shapes

Variations that generate specific shapes using polar coordinates. Unlike normal blurs, which ignore the input point, these variations are half blurs that take the angle of the input point (theta) and compute a random distance (rho) within the shape. This allows some flexibility in coloring. They can be substituted for normal blurs in many flames; if it doesn’t work, try adding some pre_blur to the transform to generate random angles (this is done for the examples here).

Download Sample flames and resources

cannabiscurve_wf

Shape resembling a cannabis leaf.

Type: 2D half blur
Author: Andreas Maschke (thargor6)
Date: 15 Jan 2012

ParameterDescription
filledDensity of the filling, from 0 (not filled, just an outline) to 1 (filled with maximum density); prior to JWildfire version 7.0.0, the value had to be 0 or 1

Cannibis Curve on MathWorld

cloverleaf_wf

Shape resembling a four leaf clover.

Type: 2D half blur
Author: Andreas Maschke (thargor6)
Date: 15 Jan 2012

ParameterDescription
filledDensity of the filling, from 0 (not filled, just an outline) to 1 (filled with maximum density); prior to JWildfire version 7.0.0, the value had to be 0 or 1

conic / conic2

Conic section shape (ellipse, parabola, or hyperbola)

Type: 2D half bluf
Author: cyberxaos
Date: 28 Jan 2007

Note that there is a different variation named “conic” which different from this one. This is probably why the Apophysis plugin is named conic2 (the variation is named “conic” in Apophysis versions where is it built-in, as well as JWildfire). There is also a variation named “Z_conic” which is the same as this one.

ParameterDescription
eccentricityDetermines the conic section type: 1 for a parabola, less for an ellipse, more for a hyperbola.
holesSet to 0.5 to generate two shapes, the main one on the left and one turned 180° on the right (a hyperbola naturally includes both). Set to 0 or 1 to show only the left or right shape. Go past 0 or 1 to create a hole.

Apophysis plugin
Conic section on Wikipedia
Understanding Conic video tutorial

japanese_maple_leaf

Shape resembling a Japanese maple leaf.

Type: 2D half blur
Author: Andreas Maschke (thargor6)
Date: 7 Aug 2021

ParameterDescription
filledDensity of the filling, from 0 (not filled, just an outline) to 1 (filled with maximum density)

How to Draw with Math (source of the formula for this variation)

maple_leaf

Shape resembling a maple leaf.

Type: 2D half blur
Author: Andreas Maschke (thargor6)
Date: 7 Aug 2021

ParameterDescription
filledDensity of the filling, from 0 (not filled, just an outline) to 1 (filled with maximum density)

How to Draw with Math (source of the formula for this variation)

oak_leaf

Shape resembling an oak leaf.

Type: 2D half blur
Author: Andreas Maschke (thargor6)
Date: 7 Aug 2021

ParameterDescription
filledDensity of the filling, from 0 (not filled, just an outline) to 1 (filled with maximum density)

How to Draw with Math (source of the formula for this variation)

shape

General shape generator using the superformula.

Type: 2D half blur
Author: cyberxaos
Date: 18 Feb 2007

The shape variation was later incorporated into the super_shape variation using the rnd parameter.

ParameterDescription
mNumber of corners
n1, n2, n3Shaping variables
a, bStretch or contract the shape
holesPuts a hole in the center if less than 0. (Although the default is 1, it works best to use 0 for no hole and a negative value to add a hole.)

Superformula entry on Wikipedia
Description and examples by Paul Bourke
Lazysusan-Shape Apophysis script



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

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