https://simonsfoundation.org/features/science-news/biologists-home-in-on-turing-patterns/

Was Alan Turing right about the mechanism behind tiger stripes?

In 1952, Alan Turing, a British mathematician best known for his work on code-breaking and artificial intelligence, was convicted of engaging in homosexual acts and sentenced to chemical castration. Amid that personal drama, he still found the time to publish a visionary paper on the mathematics of regularly repeating patterns in nature, which could be applied to the stripes on tigers and zebra fish, the spots on leopards and the spacing in rows of alligator teeth, to name a few.

Now, more than 60 years later, biologists are uncovering evidence of the patterning mechanisms that Turing proposed in his paper, prompting a resurgence of interest in them, with the potential to shed light on such developmental questions as how genes ultimately make a hand. “That structure is there,” said Jeremy Green, a developmental biologist at King’s College London. “We just need to put the chemistry onto the mathematics to get the biology.”

For the work that led to his 1952 paper, Turing wanted to understand the underlying mechanism that produces natural patterns. He proposed that patterns such as spots form as a result of the interactions between two chemicals that spread throughout a system much like gas atoms in a box do, with one crucial difference. Instead of diffusing evenly like a gas, the chemicals, which Turing called “morphogens,” diffuse at different rates. One serves as an activator to express a unique characteristic, like a tiger’s stripe, and the other acts as an inhibitor, kicking in periodically to shut down the activator’s expression.

To explain Turing’s idea, James Murray, emeritus professor of mathematical biology at the University of Oxford and an applied mathematician at Princeton, imagined a field of dry grass dotted with grasshoppers. If the grass were set on fire at several random points and no moisture were present to inhibit the flames, Murray said, the fires would char the entire field. If this scenario played out like a Turing mechanism, however, the heat from the encroaching flames would cause some of the fleeing grasshoppers to sweat, dampening the grass around them and thereby creating periodic unburned spots in the otherwise burned field.

more on link:

There’s an incredibly useful comment at the end of that link…

You can get Turing’s ’The chemical basis of morphogenesis’ from Philosophical Transactions of the Royal Society of London, at the Turing archives . The paper is quite readable by the non-specialist.

Much progress has been made in the study of the mathematics underlying Turing’s model since he published that paper. Wikipedia has a reasonable introduction.

poikilotherm said:

There’s an incredibly useful comment at the end of that link…

you mean (dah dah daaahhhh..) they’re only hypotheses generated from a limited range of parameters and are not THE TRUTH?

neomyrtus_ said:

poikilotherm said:

There’s an incredibly useful comment at the end of that link…

you mean (dah dah daaahhhh..) they’re only hypotheses generated from a limited range of parameters and are not THE TRUTH?

:)

Note that Turing’s paper on morphogenesis predates the Watson and Crick paper on DNA, so biological information theory was still in its infancy at that time. Turing wasn’t claiming to have the ultimate theory of morphogenesis, but he did show that a wide variety of animal coat patterns could arise from a fairly simple mechanism that required only a very small amount of inherited information.

These days, we are used to the idea from chaos theory that complex effects can arise from simple causes, but it wasn’t so long ago that it was usual to assume that complex effects require complex causes to generate them. Turing wasn’t the first mathematician to realize that complexity can arise in systems with simple specifications, but he was certainly a notable pioneer in this field.

He was able to test his pattern-generating recipes on a computer with a tiny amount of memory and very basic printing ability. He knew that these tests didn’t really prove anything about the actual mechanisms that LIFE uses to make patterns; still, he was quite excited by the results he obtained. He got so used to analyzing these patterns in binary form that he’d often not even bother to convert the binary data to a more pictorial format. :)

http://www.wired.com/wiredscience/2011/02/turing-patterns/

nice little infographic journey

are you one of those cyber stalkers neo?

> Turing wanted to understand the underlying mechanism that produces natural patterns. He proposed that patterns such as spots form as a result of the interactions between two chemicals that spread throughout a system much like gas atoms in a box do, with one crucial difference. Instead of diffusing evenly like a gas, the chemicals, which Turing called “morphogens,” diffuse at different rates. One serves as an activator to express a unique characteristic, like a tiger’s stripe, and the other acts as an inhibitor, kicking in periodically to shut down the activator’s expression.

As PM 2Ring says, the above is correct. The method devised by Turing has worked remarkably well in explaining the patterns of the coats of many mammals.