# 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).

## cannabiscurve_wf

Shape resembling a cannabis leaf.

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

Cannibis Curve on MathWorld

## cloverleaf_wf

Shape resembling a four leaf clover.

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

## 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.

## japanese_maple_leaf

Shape resembling a Japanese maple leaf.

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

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

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

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.

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.