Trends and variation in vertebrate patterns as outcomes of self-organization.

In extant vertebrates, natural motifs such as coat markings, spongy bone structures, neuronal arborescence or collective swarms correspond to diverse pattern types, from fractals to periodic stripes or tessellations, and so on. In this subphylum, evolution produced an apparent paradox: a given pattern may vary tremendously in its extent, periodicity or regularity, but follows general geometrical trends and is produced with meticulous precision. In this review, we discuss the role of self-organization, a patterning strategy in which spontaneous order arises through local interactions without gradient formation, in shaping both natural pattern differences and common themes. Mathematical models evidenced a wide high adaptability of self-organizing dynamics, long-advocating for their contribution to natural pattern diversity. Recent empirical and theoretical approaches taking into account network topologies and natural variation also replaced outcomes of self-organization in more constrained biological contexts, shedding light on mechanisms ensuring pattern fidelity.