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Animal patterns follow a mathematical formula

Many animals have stripes or patterns for the purposes of camouflage. But why the particular designs? Harvard researchers believe they know how a certain direction occurs and they have come up with a statistical model. Animal stripes appear when interacting substances create waves of high and low concentrations of a substance. This can be a pigment, chemical, or type of cell.

Work to explain, for example, why a tiger has parallel stripes, evenly spaced and perpendicular to the spine, has been ongoing since the 1950s (the problem, for example, was looked at by the ‘father of computing’ Alan Turing; a line of inquiry that led to Turing’s reaction-diffusion model.) It has taken nearly sixty years for the explanatory equation to be produced. Be warned, though, it all remains very theoretical.

One part of the model looks at why stripes are orientated in a particular direction. For example, why the stripes of a tiger are perpendicular to its body

And why those of the zebrafish stripes are horizontal.

Zebrafish (Danio rerio)  an small tropical aquarium fish used in molecular genetics and medical rese...

Zebrafish (Danio rerio), an small tropical aquarium fish used in molecular genetics and medical research.
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The model predicts three main factors that affect how stripes orient. These are:

1. The “production gradient,” a term for a substance that amplifies stripe pattern density;
2. The “parameter gradient,” which describes a substance that changes one of the parameters involved in forming the stripe;
3. A physical change to the molecular, cellular, or mechanical origin of the stripe.

The model shows that it only takes a very small change to switch from stripes going in one direction (say horizontal) to another (say vertical.) What the model cannot answer, and this remains a wonder of nature, is exactly why an animal ends up with stripes in a particular direction. This probably occurs at the molecular genetic level and will be a process unique to each species.

The research is published in the journal Cell Systems. The paper is titled “Orientation of Turing-like Patterns by Morphogen Gradients and Tissue Anisotropies.”

Written By

Dr. Tim Sandle is Digital Journal's Editor-at-Large for science news. Tim specializes in science, technology, environmental, and health journalism. He is additionally a practising microbiologist; and an author. He is also interested in history, politics and current affairs.

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