Secret of Lizard Camouflage: a Simple Mathematical Equation

upstart writes:

Secret of Lizard Camouflage: A Simple Mathematical Equation:

[...] A complex system is composed of several elements (sometimes only two) whose local interactions lead to global properties that are difficult to predict. The result of a complex system will not be the sum of these elements taken separately since the interactions between them will generate an unexpected behavior of the whole. The group of Michel Milinkovitch, Professor at the Department of Genetics and Evolution, and Stanislav Smirnov, Professor at the Section of Mathematics of the Faculty of Science of the UNIGE, have been interested in the complexity of the distribution of colored scales on the skin of ocellated lizards[*].

[...] The individual scales of the ocellated lizard (Timon lepidus) change color (from green to black, and vice versa) over the course of the animal's life, gradually forming a complex labyrinthine pattern as it reaches adulthood. The UNIGE researchers have previously shown that the labyrinths emerge on the skin surface because the network of scales constitutes a so-called 'cellular automaton'. "This is a computing system invented in 1948 by the mathematician John von Neumann in which each element changes its state according to the states of the neighboring elements," explains Stanislav Smirnov.

In the case of the ocellated lizard, the scales change state - green or black - depending on the colors of their neighbors according to a precise mathematical rule. Milinkovitch had demonstrated that this cellular automaton mechanism emerges from the superposition of, on one hand, the geometry of the skin (thick within scales and much thinner between scales) and, on the other hand, the interactions among the pigmentary cells of the skin.

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