Fractal Flames Community and Resources
There are many variations of JWildfire and understanding them can be a challenge. It is useful to explore the different variations and their history before using this software for your next work. To help, Rick Sidwell has created a series of articles on popular JWildfire variations and the mathematics and theory behind them.
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:
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.
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. When a new transform is created, it is assigned a variation of linear3D with an amount of 1, which just maps the input to the output without any change.
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. It also forms the basis of the gaussian_blur variation in JWildfire.
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 how the density is distributed across the disk. Blur has high density in the center, gradually decreasing towards the edge.
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.
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.