Fractal flames are a member of the iterated function system class of fractals created by Scott Draves in 1992. Draves' open-source code was later ported into Adobe After Effects graphics software and translated into the Apophysis fractal flame editor.

Fractal flames differ from ordinary iterated function systems in three ways:

The tone mapping and coloring are designed to display as much of the detail of the fractal as possible, which generally results in a more aesthetically pleasing image.

The algorithm consists of two steps: creating a histogram and then rendering the histogram.

First, one iterates a set of functions, starting from a randomly chosen point P = (P.x,P.y,P.c), where the third coordinate indicates the current color of the point.

In each iteration, choose one of the functions above where the probability that F_j is chosen is p_j. Then one computes the next iteration of P by applying F_j on (P.x,P.y).

Each individual function has the following form:

where the parameter w_k is called the weight of the variation V_k. Draves suggests that all ${\displaystyle w_{k}}$:s are non-negative and sum to one, but implementations such as Apophysis do not impose that restriction.