Of the same stripe: Turing patterns link tropical fish and bismuth crystal growth

(Press-News.org) One of the things the human brain naturally excels at is recognizing all sorts of patterns, such as stripes on zebras, shells of turtles, and even the structure of crystals. Thanks to our progress in math and the natural sciences, we are not limited to just seeing the patterns; we can also understand how they readily originate out of pure randomness.

A notable example of different natural patterns with a single mathematical explanation are Turing patterns. Conceived in 1952 by the renowned mathematician Alan Turing, these patterns arise as the solutions to a set of differential equations that describe the diffusion and reaction of chemicals satisfying a few conditions. Going well beyond pure chemistry, Turing demonstrated that such equations explain, to a remarkably precise degree, how spots, stripes, and other types of macroscopic patterns appear spontaneously in nature. Turing patterns also play a role in morphogenesis--the process by which living organisms develop their shape. Surprisingly, the underlying mechanisms behind Turing patterns are preserved across vastly different scales, from centimeters in animal pigmentation to micrometers in purely chemical systems. Does this mean that Turing patterns could be found at the nanometer scale, in the positions of individual atoms?

Associate Professor Yuki Fuseya from the University of Electro-Communications, Japan, has recently found that the answer is a resounding yes! A specialist on bismuth (Bi) and its applications in condensed-matter physics, Dr. Fuseya never imagined working with Turing patterns, which are mostly studied in mathematical biology. However, on noticing some mysterious periodic stripes he had seen in Bi monoatomic layers, Dr. Fuseya got the wild idea they might actually be Turing patterns. And after three years of trial and error, he finally found success!

In a study published in END