Variation Information

## Fractal Flame Variation Guide Part 2

List of the common fractal variations, their parameters and examples.

## Flame Fractal Variation Guide Part 1

A guide to the more common variations and their parameters.

## Fractal Variation List

Long list of variations used in JWildfire and Apophysis. Parameter meanings and website links for further information.

## disc

The disc variation is based on polar coordinates, where points are specified by a distance ρ and an angle θ. The basic idea is simple: it just switches ρ and θ (after scaling by π to make things work nicely). This converts wedges centered at the origin to half-rings and vice versa as shown below. The images on the left side are before and on the right side after disc is applied.

## splits

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

## julian

The julian variation is a popular one for flames, and the basis of many styles. The basics of julian and some related variations are described.

## fract variations

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 the flame, escape-time fractals use the orbit of a point to determine how to color it, commonly by determining how long it takes the orbit to cross an imaginary circle (or to “escape”; hence the name “escape-time”). The two methods usually generate very different fractals.

## Elliptic

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 variations to make interesting flames.

## unpolar and foci

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.

## bipolar

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. Although their mathematical application is specialized, they can be used in variations to make interesting flames. Rectangular coordinates are based on two families of parallel lines (horizontal and vertical) where each line in the first family intersects each line in the other at a right angle.

## polar Variation Information

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! Understanding them can help us use these variations more effectively.

## text_wf

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. The brain processes words differently from images, so this can add a new level of depth to fractal flames. Or the text can be a single symbol (not necessarily a letter), using text_wf as a blur with a specialized shape. Text_wf can be quite versatile.