Fractal dimensions of cranial sutures and waveforms.

ABSTRACT

Two quite different shapes of cranial sutures ostensibly yield fractal dimensions. The rare, intricate sutures yield the more valid fractal dimensions because self-similar scaling provides a double-log plot of negative slope. These sutures are fractals over a range of several r values. Some of the highly folded, wavy sutures in humans also fill space except at very tiny values of r, but are nonfractal. A great deal depends on whether the dimension D is > 1 and by how much, whether the curve yields a false fractal dimension, whether the curve scales and shows self-similarity, and whether the scaling occurs regularly in the same pattern. We suggest careful attention to the inverse power law equations, which when misused can yield false fractal values. Cranial sutures vary from the simple wavy sutures to the complex folded ones, and, in rare instances, evolve and develop to the self-similar, scaling, elaborate ones called intricate sutures. The main thing is to express the biology precisely, whether waveform regularity or irregularity or scaling elaboration conserving space and the original shape. D values may not in themselves reliably allow such a distinction, by whatever method used.