Z manipulation
Variations that manipulate only the z coordinate. All of these must be used with another variation to process x and y (even if linear to simply copy it).
Variation Types
JWildfire makes it simple to experiment with different variations of a fractal flame in real time. All of them have their own set of advantages and disadvantages, which vary based on the type of design for which they are intended, but there are hundreds of various methods to construct them. This page contains descriptions of some of the most frequent types or groupings of variations, as well as cross-references to additional resources that will assist you in learning more about them.
Rick Sidwell is always to be thanked for all of the information that he has given us.
Waves
Variations that add waves to x, y, and/or z. There are a lot of different variants on this theme, differing in the parameters available and how they are applied.
Synth
Variations that emulate a number of other variations, adding wavy effects using a technique from audio synthesizers.
Shapes
Variations that ignore the input and generate specific shapes. Often called “blurs” because they create a blur effect when used on the same transform with other variations.
Rosecurve
The rose or rhodonea curve is shaped like a flower with petals, obtained by plotting a sine curve in polar coordinates. Its shape is determined by the frequency of the sine wave, denoted k.
Reshapers
Variations that reshape the input (for example, turn a circle into a square or other polygon).
Plotting
These variations are all blurs that plot formulas in two or three dimensions. They allow entering custom formulas, but also come with presets for ease of use.
Meshes
Variations that generate meshes, three dimensional shapes made from connected triangles. These are all blur variations that ignore their inputs. They are most useful for solid renders, though they work for normal flames as well.
Maurer Lines
Maurer lines extend the Maurer rose with different types of curves, rendering methods, and coloring.
Julia
Variations based on polynomial Julia sets. For escape time fractals, the formula is z → z^n + c. For flames, the mapping is reversed and the “+ c” part is done by the affine transform, so these variations basically take the root of the input taken as a complex number, returning one of the results at random.