The locus in this screenshot is the image of the dashed circle under 8 applications of the following function: a point is inverted about each of the three points arranged in an equilateral triangle in the center (inversion radius is the length of the segment in the top left corner) and the new point is the centroid of the triangle formed. (In case you're wondering where I got this function, I did my highschool thesis on analyzing a variant of it.)

This shows the benefit of adaptive sampling: the locus is extremely non-uniform and without adaptive sampling, we would see only a few points (even for many thousands of samples). As it is, it looks acceptable on KSEG with 2000 samples (the screenshot shows about 10000--and it looks perfect). With 2000 samples, KSEG can redraw this locus a couple of times per second (on my 2 yr old PII 350). I'd like to see another geometry program interactively render a locus this complex! I won't even mention that this took me less than four minutes to construct. Ok, I just did :-). This file is included with the examples as largelocus.seg. The construction used to generate it is invert3.sec.