The same is real for the labyrinthine patterns formed by the green or black scales of the ocellated lizard. 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 actually been interested in the intricacy of the distribution of colored scales on the skin of ocellated lizards.
Ocellated lizard.
A multidisciplinary group at the UNIGE has succeeded in describing the intricate circulation of scales in the ocellated lizard by ways of a basic equation.
The shape-shifting clouds of starling birds, the organization of neural networks or the structure of an anthill: nature has plenty of complex systems whose habits can be designed utilizing mathematical tools. The same is real for the labyrinthine patterns formed by the green or black scales of the ocellated lizard. A multidisciplinary team from the University of Geneva (UNIGE) explains, thanks to an extremely basic mathematical formula, the complexity of the system that generates these patterns. This discovery adds to a much better understanding of the advancement of skin color scheme: the process permits several areas of green and black scales but always results in an optimum pattern for the animal survival. These results are released in the journal Physical Review Letters.
An intricate system is made up of several elements (in some cases only two) whose regional interactions lead to worldwide homes that are difficult to forecast. The result of a complex system will not be the sum of these elements taken independently since the interactions between them will generate an unanticipated habits of the entire. 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 actually had an interest in the intricacy of the circulation of colored scales on the skin of ocellated lizards.
The private scales of the ocellated lizard (Timon lepidus) change color (from green to black, and vice versa) over the course of the animals life, gradually forming a complicated labyrinthine pattern as it reaches the adult years. The 3 UNIGE researchers identified that this design can properly describe the phenomenon of scale color change in the ocellated lizard. In the case of the ocellated lizard, the procedure of color change prefers the formation of all distributions of green and black scales that each time outcome in a labyrinthine pattern (and not in lines, areas, circles, or single-colored areas …).
A multidisciplinary team has prospered in describing the complicated distribution of scales in the ocellated lizard by ways of a simple equation.
Labyrinths of scales
The specific scales of the ocellated lizard (Timon lepidus) modification color (from green to black, and vice versa) throughout the animals life, gradually forming a complicated labyrinthine pattern as it maturates. The UNIGE researchers have previously shown that the labyrinths emerge on the skin surface due to the fact that the network of scales makes up a so-called cellular robot. “This is a computing system invented in 1948 by the mathematician John von Neumann in which each aspect alters its state according to the states of the nearby components,” discusses Stanislav Smirnov.
In the case of the ocellated lizard, the scales alter state– green or black– depending on the colors of their next-door neighbors according to an accurate mathematical guideline. Milinkovitch had actually shown 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 amongst the pigmentary cells of the skin.
The patterns of the ocellated lizard are foreseeable by a mathematical model.
The roadway to simpleness
Szabolcs Zakany, a theoretical physicist in Michel Milinkovitchs lab, partnered with the 2 professors to figure out whether this change in the color of the scales could obey an even simpler mathematical law. The researchers thus relied on the Lenz-Ising model developed in the 1920s to explain the behavior of magnetic particles that possess spontaneous magnetization. The particles can be in two different states (+1 or -1) and communicate only with their very first neighbors.
” The sophistication of the Lenz-Ising model is that it describes these characteristics using a single formula with only two criteria: the energy of the aligned or misaligned neighbors, and the energy of an external electromagnetic field that tends to push all particles towards the +1 or -1 state,” explains Szabolcs Zakany.
An optimal disorder for a better survival
The 3 UNIGE researchers determined that this design can properly explain the phenomenon of scale color change in the ocellated lizard. In the case of the ocellated lizard, the process of color modification favors the development of all circulations of green and black scales that each time outcome in a labyrinthine pattern (and not in lines, areas, circles, or single-colored locations …).
” These labyrinthine patterns, which provides ocellated lizards with an optimal camouflage, have actually been chosen in the course of advancement. These patterns are generated by an intricate system, that yet can be simplified as a single formula, where what matters is not the exact place of the green and black scales, but the basic look of the final patterns,” excites Michel Milinkovitch. Each animal will have a different accurate area of its green and black scales, however all of these alternative patterns will have a comparable look (i.e., an extremely similar energy in the Lenz-Ising design) giving these different animals comparable chances of survival.
Referral: “Lizard Skin Patterns and the Ising Model” by Szabolcs Zakany, Stanislav Smirnov and Michel C. Milinkovitch, 27 January 2022, Physical Review Letters.DOI: 10.1103/ PhysRevLett.128.048102.