Multifractal signatures in ossification reveal a disordered-to-ordered transition in mineral pattern

Abstract

Developing biological systems can exhibit both dynamic pattern formation and cross-scale interactions. Multiscale relationships are critical in the establishment of these patterns but remain poorly understood. Classification of mineral pattern in bone is a quintessential example. One approach to quantifying these patterns relies upon statistical self-similarity and, in particular, monofractal analysis. However, simple monofractal characterisations fail to capture the complexity of multiscale interactions in developing biological systems. Here we show that multifractal techniques, effectively capture the complex patterns of self-similarity in a dimensionally reduced, usable way. Further, we show that a simple generative model of ossification in the mouse skull, coupled with multifractal methods indicates a primary role of collagen density in pattern establishment and predicts the existence of a sharp boundary in pattern complexity.