New York Times, by Stephh Yin, 4/12/17
The ocellated lizard — known as the jeweled lacerta in the pet trade — is born rusty brown with white polka dots. Within a few months, its skin begins to change into a dizzying, labyrinthine array of black and bright green pixels. By the time the lizard has sexually matured, reaching up to two feet in length, some 4,000 scales along its back are all black or green, possibly to accommodate a habitat change between early life and adulthood. Through the rest of the lizard’s life, many of these scales will continuously flip between black and green.
These outfit changes are dazzling in their own right. But even more surprisingly, the lizard’s patterns may unfold like a computer simulation, according to a study published in Nature on Wednesday.
Studying ocellated lizards, Michel Milinkovitch, a professor of genetics and evolution at the University of Geneva, noticed the animals’ scales seemed to behave like a cellular automaton, a rule-based model often used in computer science. The general rule was that green scales tended to have four black neighbors, and black scales tended to have three green neighbors.
Though cellular automata are commonly used to simulate biological systems on computers, this is the first example of a “living cellular automaton,” said Dr. Milinkovitch, an author of the paper.
Cellular automata were discovered in the 1940s by John von Neumann and Stanislaw Ulam, then mathematicians at the Los Alamos National Laboratory, who wanted to build a self-replicating machine. An extremely simple cellular automaton, according to Andy Ilachinski, author of Cellular Automata: A Discrete Universe, who was not involved in the study, is a string of lights where each light switches between on and off depending on what its neighbors are doing. With more complex rules, cellular automata can be used to model many things, from snowflake formation to traffic
To look for a cellular automaton in ocellated lizards, Dr. Milinkovitch, with Liana Manukyan and Sophie Montandon, then graduate students, collected high-resolution scans of three lizards’ bodies from hatchling stages to adulthood. From this, the researchers inferred a set of rules — a cellular automaton — for how the scales changed color. If a green scale had many green neighbors, there was a high probability it would turn black. If it had no green neighbors, it would stay green.
Simulating their cellular automaton, the researchers found it generated a pattern indistinguishable from real lizard patterns. Next, they wondered how the lizards were making these patterns. Their answer came from another mathematician: Alan Turing, pioneer of computer science and artificial intelligence.
In the 1950s, Mr. Turing mathematically modeled how patterns and shapes take form in living things. Called a reaction-diffusion system, his model proposed that patterns emerge from a feedback loop between chemicals that spread through a space, activating and inhibiting each other. His mechanism has since been demonstrated in many organisms. In zebrafish, Turing interactions between cells containing different colors of pigment have been shown to generate stripes.
Dr. Milinkovitch suspected a similar Turing mechanism was at play in ocellated lizards. But when he transferred the zebrafish model to lizards, the patterns that emerged were off. Instead of pixelated designs, with each scale being discretely green or black, they were smooth designs, with many scales containing both colors.
It looked as if the lizard’s skin were a flat canvas, as opposed to a scaly one with ridges and valleys, Dr. Milinkovitch thought. His team re-simulated the Turing mechanism, this time accounting for how the valleys between lizard scales might impede the flow of signals between pigmentary cells of different colors. Remarkably, the pattern that emerged behaved like a cellular automaton. To solidify this link, Stanislav Smirnov, a mathematics professor at the University of Geneva, created a set of Turing equations that reproduced the cellular automaton behavior observed.
Tracking an animal’s pattern in fine detail over a long period of time to infer the “rules” that govern the pattern is “a great example of computational imaging,” said Leah Edelstein-Keshet, a professor of mathematics at the University of British Columbia, who was not involved in the research. “I had never seen anything like this before.”