Fractal flames are a type of iterated function systems invented by Scott Draves in 1992. The fixed sets of fractal flames may be computed using the chaos game (as described in an earlier post), and the resulting histogram may be visualised as beautiful fractal-like images. If the histogram also has a dimension storing what function from the function system was used to get to a particular point, it may even be coloured.

There are a lot of software available to generate fractal flames, and I have built yet another one focussed on generating very high resolution images for printing. The image below has resolution 7087 x 7087 and been generated after about 4 hours of computation on a laptop. It is free to use under a Creative Commons BY-NC 4.0 license.

References

Scott Draves & Eric Reckase (2003), The Fractal Flame Algorithm, https://flam3.com/flame_draves.pdf