Continuing my learning/research of fractals, today I've finally managed to render something that looks like Fractal Flame. AFAIK the most important paper on this subject is The Fractal Flame Algorithm by Scott Draves and Erik Reckase. According to this document, I've first added to my program the ability to use colors, so each point, as it has the position iteratively processed by some functions, also carries current color. Now I am able to render colourful IFS fractals:
Implementing logarithmic tone mapping and gamma correction significantly improved quality. Colors can help visualising internal structure of a fractal:
Next I've coded (almost) all functions mentioned in this paper, so now not only affine transforms are possible in my program. This allows me to mix traditional fractals with new functionality:
And finally to render something that looks like famous Fractal Flames. But it's not easy to achieve this. Modifying numeric parameters in a text file is not convenient, and even if I had an editor with real-time preview, it's not obvious what parameters give what results and whether they will degenerate to something like a single point. There are simply too many degrees of freedom :) If we had a continuous function Beauty(Params), we could use some optimization algorithms to find and render its local extrema :) Anyway, here are my first renders (more in Fractal Flames Gallery).