Iâ€™ve been working on getting a Mandelbrot version of the IFS fractals working. Unfortunately Iâ€™ve run into some major snags with the approach. I havenâ€™t come up with a fast deterministic approach to detect if a particular point is in one of these fractals. Iâ€™ve been trying to build a single inverse map built by stitching together inverses of functions chosen using voronoi domains. That works for non-overlapping functions but breaks down for the overlapping case.
This results in clipping occurring at the overlaps. While it can create some interesting effects on itâ€™s own, it is definitely not what Iâ€™m looking for.
My next approach to solve this issue was to try to converge on a particular point using forward iteration. Â The corresponding issue for that one is that there isnâ€™t any way to develop nested sets or any kind of convergence path. In order to get to a point x you might have to converge over to a point over in another region of the fractal and then hop over to the point in question. It seems the only way to make this really work is to reverse iterate every combination of maps trimming the set as the points leave the cutoff circle. In the mean time I like some of the renderings Iâ€™ve generated from my tests.