Detailed Variation Articles

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These are the detailed articles about some of the variations used in JWildfire, kindly researched in depth and supplied by Rick Sidwell and Jesus Sosa. Essential reading for those wanting to dig even deeper into the intricacies of fractal flame variations.

 

variations

bipolar

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…

Blob

Blob

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…

blur

blur

Description The blur variation generates a filled-in circle. Unlike most variations, which transform the plane by mapping input points to output points, blur completely ignores the input. The variations blur_circle, circleblur, and sineblur also generate filled-in circles. They differ in…

disc

disc

Introduction 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…

Elliptic

Elliptic

Description The most commonly used coordinate systems are rectangular coordinates and polar coordinate. But these aren’t the only possibilities. One of the less common coordinate systems is elliptic coordinates. Although their mathematical application is specialized, they can be used in…

fract variations

fract variations

Description Escape-time fractals are in a way the opposite of flame fractals. Both use the idea of an orbit: the sequence of points generated by repeatedly iterating fractal formulas. But while flame fractals plot the actual orbit points to create…

gaussian_blur

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…

glynnSim

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…

julian

julian

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. It is most easily understood using polar coordinates (see polar), where…

linear

linear

[latexpage] 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…

polar

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…

spherical

spherical

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…

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