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Professor discusses symmetry, patterns in nature

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A leopard is chasing a zebra, bound to follow the laws of nature and natural selection, down a sand dune and across a plain of dried mud, bound to the laws of geology and sediments.

The stripes of the zebra are akin to the ripples in the sand dune, and the leopard’s spots look similar to the cracks in the dried mud.

These similarities hint at another set of natural laws that binds both animal and mineral together — the laws of mathematics.

“What mathematics does is provide a menu of patterns — which ones appear depends on physics,” said Marty Golubitsky, Ohio State professor of natural and mathematical sciences and director of the Mathematical Biosciences Institute. “Pattern formation is both a mathematical and a physics of biology subject.”

Golubitsky gave a lecture on patterns in nature and their mathematical underpinnings at OSU on Sunday.

Held in the Ohio Union U.S. Bank Conference Center, the lecture drew about 300 people and was a part of the Science Sundays Lecture series with the OSU College of Arts and Sciences.

“It’s a way for people to see mathematics in pictures, which is much easier to understand,” Golubitsky said. “Why are the patterns so similar in physically, biologically completely different situations.”

Soon after saying this, he asked the audience if any of them knew what was in a photo on his lecture slide.

Someone answered that it was a photo of vertical erosion formations of the rock basalt, but it turned out to be a photo of corn starch that had taken a very similar form after being wetted and left to dry.

Golubitsky said that drug-induced geometric visual hallucinations also have a common pattern system and this might be due to an attribute of the visual cortex that is common among people.

Also having mathematical symmetry are the locomotive rhythms of four-legged animals.

“I can distinguish a hop from a walk by their symmetries,” Golubitsky said.

He said the study of animal gaits has led to new networks of differential equations.

Golubitsky also said chaos is not an idea that is well understood in terms of mathematics and science. The trajectory of a function on a plane, such as a Cartesian coordinate system, can be chaotic but will still have dependence on initial conditions.

This was illustrated in the lecture with symmetrical, computer-generated patterns that had been formed by such functions what had gone across a plane several million times.

“The stuff about chaos theory, that was definitely interesting, all these chaotic processes lead to recognizable patterns,” said Brennan Barrington, a third-year in aerospace engineering.

Golubitsky was given approximately 24 hours’ notice before giving this lecture because the scientist who was originally scheduled to appear fell ill and was unable to come to OSU.

He said that if students are interested in science, he wants them to be aware that patterns are present in the work they are doing, and they should also think about symmetry.

An audience member asked if Golubitsky knew of any symmetry in human behavior.

“In terms of behavior, haven’t a clue,” he said.

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