Why imperfection could be key to Turing patterns in nature

Many Turing mechanism models yield too-perfect patterns; varying cell sizes vastly improves the results.

A mixture of two types of pigment-producing cells undergoes diffusiophoretic transport to self-assemble into a hexagonal pattern. Credit: Siamak Mirfendereski and Ankur Gupta/CU Boulder

A zebra’s distinctive black-and-white stripes, or a leopard’s spots, are both examples of “Turing patterns,” after mathematician and computer scientist Alan Turing, who proposed an intriguing hypothetical mechanism for how such complex, irregular patterns might emerge in nature. But Turing’s original proposal proved too simplified to fully recreate those natural patterns. Scientists at the University of Colorado at Boulder (UCB) have devised a new modeling approach that achieves much more accurate final patterns by introducing deliberate imperfections, according to a new paper published in the journal Matter.

Turing focused on chemicals known as morphogens in his seminal 1952 paper. He devised a mechanism involving the interaction between an activator chemical that expresses a unique characteristic (like a tiger’s stripe) and an inhibitor chemical that periodically kicks in to shut down the activator’s expression. Both activator and inhibitor diffuse throughout a system, much like gas atoms will do in an enclosed box. It’s a bit like injecting a drop of black ink into a beaker of water. Normally, this would stabilize a system, and the water would gradually turn a uniform gray. But if the inhibitor diffuses at a faster rate than the activator, the process is destabilized. That mechanism will produce spots or stripes.

Scientists have tried to apply this basic concept to many different kinds of systems. For instance, neurons in the brain could serve as activators and inhibitors, depending on whether they amplify or dampen the firing of other nearby neurons—possibly the reason why we see certain patterns when we hallucinate. There is evidence for Turing mechanisms at work in zebra-fish stripes, the spacing between hair follicles in mice, feather buds on a bird’s skin, the ridges on a mouse’s palate, and the digits on a mouse’s paw.

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Why imperfection could be key to Turing patterns in nature

Many Turing mechanism models yield too-perfect patterns; varying cell sizes vastly improves the results.

A mixture of two types of pigment-producing cells undergoes diffusiophoretic transport to self-assemble into a hexagonal pattern. Credit: Siamak Mirfendereski and Ankur Gupta/CU Boulder

A zebra’s distinctive black-and-white stripes, or a leopard’s spots, are both examples of “Turing patterns,” after mathematician and computer scientist Alan Turing, who proposed an intriguing hypothetical mechanism for how such complex, irregular patterns might emerge in nature. But Turing’s original proposal proved too simplified to fully recreate those natural patterns. Scientists at the University of Colorado at Boulder (UCB) have devised a new modeling approach that achieves much more accurate final patterns by introducing deliberate imperfections, according to a new paper published in the journal Matter.

Turing focused on chemicals known as morphogens in his seminal 1952 paper. He devised a mechanism involving the interaction between an activator chemical that expresses a unique characteristic (like a tiger’s stripe) and an inhibitor chemical that periodically kicks in to shut down the activator’s expression. Both activator and inhibitor diffuse throughout a system, much like gas atoms will do in an enclosed box. It’s a bit like injecting a drop of black ink into a beaker of water. Normally, this would stabilize a system, and the water would gradually turn a uniform gray. But if the inhibitor diffuses at a faster rate than the activator, the process is destabilized. That mechanism will produce spots or stripes.

Scientists have tried to apply this basic concept to many different kinds of systems. For instance, neurons in the brain could serve as activators and inhibitors, depending on whether they amplify or dampen the firing of other nearby neurons—possibly the reason why we see certain patterns when we hallucinate. There is evidence for Turing mechanisms at work in zebra-fish stripes, the spacing between hair follicles in mice, feather buds on a bird’s skin, the ridges on a mouse’s palate, and the digits on a mouse’s paw.

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Melissa set to be the strongest hurricane to ever strike Jamaica

Storm reached sustained winds of 160 mph on Monday morning.

Hurricane Melissa will make landfall in southern Jamaica less than 24 hours from now, and it is likely to be the most catastrophic storm in the Caribbean island’s history.

As it crawled across the northern Caribbean Sea on Monday morning, Melissa officially became a Category 5 hurricane with 160 mph winds, according to the National Hurricane Center.

The hurricane will likely fluctuate in intensity over the next day or so, perhaps undergoing an eyewall replacement cycle. But the background conditions, including very warm Caribbean waters and low wind shear, will support a very powerful hurricane and the potential for further strengthening.

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