My next step in Fractal Flames rendering was to enhance the way I give colors to pixels on the final texture. As positions of the points iterated through the function system are discretized to a 3D matrix, but before it's processed into the final texture, I've introduced a choice of matrix format (inspired by texture formats in DirectX).
The simplest one is MATRIX_FORMAT_DENSITY, as it has only one component per cell - a density, equal to number of points that hit this particular cell. No coloring is done here, so each pixel is just white and there is only density influencing its brightness through tone mapping.
Second format is MATRIX_FORMAT_COLOR_DENSITY. It works similar to what is described in The Fractal Flame Algorithm paper. Each processed point carries a "color" with it, but this "color" is just a scalar value in range 0..1. Every possible transform (transforms are chosen in random manner according to their probabilities) pushes the color towards its "desired" value, defined for each transform. Current point color is added to the matrix cell so that final color is an average of colors of all points that hit this cell.
To visualize this scalar "color", it's nice to process it through some lookup table, gradient, palette or however you call it. I seems easy to generate or hardcode one, but I prefer to rely on existing gradients prepared by more talented people, so I've implemented reading of two gradient formats so far: gradient from a single-row texture or from a "cmap.UGR" file shipped with Apophysis (nice, free Windows application that render fractal flames according to the paper mentioned above). I'm also planning to support "ggr" files with gradients from GIMP, but it's far more sophisticated and powerful format.
And finally there is the third way of coloring fractal flames that seems most intuitive to me - MATRIX_FORMAT_RGB_DENSITY. Here, full three color components are carried with points and saved to the matrix. Each transform pushes the point color towards its own "desired" RGB value. Thanks to this, each transform influences not only shape, but also color of the fractal in direct and observable way (like the scaling transform here, that shrinks points to the center, which is red).