# Variation backgrounds and understanding – Rick Sidwell

Gain a much better understanding of the variations of JWildfire. Rick Sidwell has started a set of articles exploring in depth the variations of JWildfire. They look at the history of how they came to be, the way they work, and have examples of how they work.

Fully recommended.

#### bipolar

Name: bipolar
Type: 2D
Author: Joel and Michael Faber

Name: bTransform
Type: 2D
Author: Michael Faber

## Description

The most commonly used coordinate systems are rectangular coordinates and polar coordinates (see polar). But these aren’t the only possibilities. One of the less common coordinate systems is bipolar coordinates.…

Name: blob
Type: 2D

## Description

The blob variation pushes and pulls the plane to make it look like a blob. Specifically, it takes a sine wave, wraps it into a circle, and uses that to distort the plane. The pictures below show respectively a sine wave, a radial sine wave (one wrapped into a circle), and a circular dc_perlin texture before and after applying blob.…

#### blur

Name: blur
Type: 2D blur

Name: blur_circle
Type: 2D blur
Author: Joel and Michael Faber

Name: circleblur
Type: 2D blur
Author: Anton Liasotskiy (zy0rg)

Name: sineblur
Type: 2D blur
Author: Anton Liasotskiy (zy0rg)

## Description

The blur variation generates a filled-in circle.…

#### disc

The disc variation is based on polar coordinates, where points are specified by a distance ρ and an angle θ (see polar). The basic idea is simple: it just switches ρ and θ (after scaling by π to make things work nicely).…

#### Elliptic

Name: elliptic
Type: 2D
Author: Joel and Michael Faber

Name: eMotion
Type: 2D
Author: Michael Faber

Name: ePush
Type: 2D
Author: Michael Faber

Name: eRotate
Type: 2D
Author: Michael Faber

Name: eScale
Type: 2D
Author: Michael Faber

## Description

The most commonly used coordinate systems are rectangular coordinates and polar coordinate.…

#### fract variations

Name: fract_dragon_wf
Type: 3D blur
Author: Andreas Maschke

Name: fract_julia_wf
Type: 3D blur
Author: Andreas Maschke

Name: fract_mandelbrot_wf
Type: 3D blur
Author: Andreas Maschke

Name: fract_meteors_wf
Type: 3D blur
Author: Andreas Maschke

Name: fract_pearls_wf
Type: 3D blur
Author: Andreas Maschke

Name: fract_salamander_wf
Type: 3D blur
Author: Andreas Maschke

## Description

Escape-time fractals are in a way the opposite of flame fractals.…

#### gaussian_blur

Name: gaussian_blur
Type: 2D blur

Name: pre_blur
Type: 2D blur pre

## Description

Carl Frederich Gauss was a preeminent early nineteenth century German mathematician and scientist. Among the many things named for him is the Gaussian distribution, also known as the normal distribution or the bell curve, which is very important in statistics.…

#### glynnSim

Name: glynnSim1
Name: glynnSim2
Name: glynnSim3
Type:2D
Author: Alexey Ermushev (eralex61)

## Description

The glynnSim variations are a cross between linear and spherical. Using the unit circle as a dividing line, their output has three parts:

• Outside the unit circle is whatever was there before (like linear),
• Inside the unit circle is a reflection across the unit circle of what was outside the unit circle (like spherical), and
• The points that were inside the unit circle are replaced with a blur:
• for glynnSim1, the blur is a disk,
• for glynnSim2, the blur is an arc, and
• for glynnSim3, the blur is the border of a ring.

#### julian

Name: julian
Type: 2D

Name: eJulia
Type: 2D
Author: Michael Faber

Name: julia
Type: 2D

Name: juliac
Type: 2D
Author: David Young (Sc0t0ma)

Name: julia3D
Type: 3D
Author: Joel Faber

Name: julia3Dq
Type: 3D
Author: Peter Sdobnov (Zueuk)

Name: julia3Dz
Type: 3D

Name: julian2
Type: 2D
Author: Georg Kiehne (xyrus02)

Name: julian3Dx
Type: 3D
Author: Georg Kiehne (xyrus02)

Name: juliascope
Type: 2D

Name: juliaq
Type: 2D
Author: Peter Sdobnov (Zueuk)

Name: phoenix_julia
Type: 2D
Author: Chris Johns (TyrantWave)

## Description

The julian variation (sometimes written juliaN to emphasize its relation with Julia sets, see below) is a popular one for flames, and the basis for many other variations.…

Name: linear3D
Type: 3D

Name: linear
Type: 2D

## Description

Although “linear” seems a strange name for a non-linear variation, it’s a really important one. The name makes sense in the context that it means not to use a non-linear variation, just the affine mappings that are part of every transform.…

#### polar

Name: polar
Type: 2D

Name: polar2
Type: 2D
Authors: Joel and Michael Faber

## Description

Polar coordinates are an alternative to the more common rectangular coordinates that simplifies the math for many applications. In fact, about about a quarter of the many JWildfire variations are based on polar coordinates!…

Name: spherical
Type: 2D

## Description

The spherical variation reflects the plane across the unit circle (the circle with radius 1 centered at the origin). Mathematically, this is called “inversion in the unit circle”. This is illustrated with the following contrived example, which uses five transforms with svg_wf to create five purple creatures (the default svg_wf graphic) in various locations.…

#### splits

Name: splits
Type: 2D
Author: Michael Faber

Name: splits3D
Type: 3D
Author: Chris Johns (TyrantWave)

Name: separation
Type: 2D
Author: Michael Faber

## Description

The splits variation splits the plane horizontally, vertically, or both, moving the halves away from the center to leave a gap.…

#### subflame

Name: subflame_wf
Type: 3D blur
Author: Andreas Maschke

## Description

The subflame_wf variation allows using a flame as part of another flame. This is useful for providing textures and filling in blank spaces. It is often possible to accomplish similar results using Xaos, but using subflames is often simpler.…

#### text_wf

Name:text_wf
Type: 2D blur
Author:Andreas Maschke

## Description

The text_wf variation incorporates a line of text into a flame. It is a blur variation like circleblur and starblur, meaning it ignores the input and just generates a shape; but instead of the shape being a circle or star, it is a line of text.…

#### unpolar and foci

Name: unpolar
Type: 2D
Author: Michael Faber

Name: foci
Type: 2D
Authors: Joel and Michael Faber

## Description

The unpolar variation is the opposite of polar2; see the polar description. Whereas polar2 treats the log-polar coordinates of a point as rectangular coordinates, unpolar treats the rectangular coordinates of a point and treats them as log-polar coordinates.…