This is one of the more interesting questions about the algorithm. While some of my earliest writings (which I have not revised) indicated that some shapes could not be fractalized, more extensive work has led me to the conclusion that any shape can be fractalized by the statistical geometry algorithm.
Various lines of reasoning, including the conclusions from the function b(c,N), show that as c decreases toward 1 the packing gets looser. Thus the only difference between shapes appears to be that compact shapes (circle, square) can be fractalized up to relatively high values of c (e.g., c around 1.52 for squares) while sprawly, noncompact shapes (e.g., rings with inner diameter only slightly less than outer diameter) have a much lower maximum c value.
Thus it is claimed by me that any shape (or sequence of shapes) can be fractalized for some value of c. As of now I am not aware of any exceptions among those shapes which have been explored by computation. It remains unclear whether this assertion can be proved by rigorous mathematics.
John Shier
December 2011