Author: Heather M. M. Hill
Compilation: Pure Jane
Image credit: Juan La Cruz/ CC BY-SA 3.0
Timon lepidus, also known as the one-eyed lizard, has patterned skin with black and green scales. During the adolescence of a lizard, each scale can change from green to black and vice versa. As it ages, its young spots change proportions one at a time, forming a labyrinth of patterns that become fixed in adulthood.
Five years ago, Michel Milinkovitch of the University of Geneva and his colleagues discovered that they could simulate the formation of T. Leimus skin patterns using a cellular automaton. The model is probably best known for John Horton Conway's Game of Life, which consists of a grid of cells, each of which evolves according to a set of rules. Now, the researchers have found a simpler description of the evolution of the pattern: the Ising model (the Ising model was originally defined for the ferromagnetic system, which correctly predicts the complex evolution of reptile skin patterns), a ferromagnetic statistically mechanical model.
The odds of any given proportion changing its color depend on its nearest scale; the scales seem to avoid sharing the same color with too many adjacent colors. A cellular automaton model of lizard skin requires a number of parameters that take the form of a probability that a scale will change from black to green or from green to black as a function of the number of adjacent black or green. But this behavior is also reminiscent of the lattice of antiferromagnetic spins: each spin is aligned with as many adjacent lattices as possible.
Image credit: S. Zakany、S. Smirnov、MC Milinkovitch、Phys。 Priest Wright. 128 , 048102 (2022)
Milinkovitch and his colleagues found that at limited temperatures in the external magnetic field, the Ising model of the antiferromagnet matched the observed lizard-scale behavior and results of the cellular automaton model, as shown in the figure. (An external magnetic field replaces the scale's slight preference for black rather than green, and the limited temperature reflects the effect of randomness in the process.) The model correctly predicts the evolution of the pattern over time, the final pattern, and the overall balance of green and black scales. It does this with an equation and two parameters.
The Ising model doesn't require any microscopic information about how cells interact, but future studies could explore how cell-level parameters affect the fitting parameters of the Ising model. The model may also be suitable for Sheila monsters and other species with colored flipped scales.