Alan Turing’s Patterns in Nature, and Beyond
Near the end of his life, the great mathematician Alan Turing wrote his first and last paper on biology and chemistry, about how a certain type of chemical reaction ought to produce many patterns seen in nature.
Called “The Chemical Basis of Morphogenesis,” it was an entirely theoretical work. But in following decades, long after Turing tragically took his own life in 1954, scientists found his speculations to be reality.
First found in chemicals in dishes, then in the stripes and spirals and whorls of animals, so-called Turing patterns abounded. Some think that Turing patterns may actually extend to ecosystems, even to galaxies. That’s still speculation — but a proof published Feb. 11 in Science of Turing patterns in a controlled three-dimensional chemical system are even more suggestion of just how complex the patterns can be.
How Turing Patterns Work
At the heart of any Turing pattern is a so-called reaction-diffusion system. It consists of an “activator,” a chemical that can make more of itself; an “inhibitor,” that slows production of the activator; and a mechanism for diffusing the chemicals.
Many combinations of chemicals can fit this system: What matters isn’t their individual identity, but how they interact, with concentrations oscillating between high and low and spreading across an area. These simple units then suffice to produce very complex patterns.
Proving Their Existence
Even though what appeared to be Turing patterns were immediately evident in nature, it wasn’t easy to be sure they were produced by reaction-diffusion systems, rather than some other mechanism.
The breakthrough came during the 1980s, when chemists were able to produce Turing patterns in the laboratory, on thin slabs of gel. In these controlled systems, the reactions could be closely followed, simulated on computers and unambiguously demonstrated as true Turing patterns.
At left in each photograph is a real seashell. At right is a computer-generated image of a pattern produced by a Turing pattern simulation.
At left in each photograph is the eye of a popper fish. At right is a computer-generated image of a pattern generated by a Turing pattern simulation.