Patterns
Credit: Cheetahs on the Edge — Director's Cut | National Geographic
Has this video called your attention? Why?
Most people would say that the movements are really beautiful, but few actually focus on the cheetah's pattern. It is mind-blowing!
There are a lot of animals who present patterns in their skin. These animals can be found everywhere in nature, from the sea to the sky. Here are some colorful examples:
For many decades, scientists didn't know how these attractive patterns were formed. They thought that genes “knew” which substance they needed to produce. However, to do so, genes had to spot their own position, but they have no way of doing that.
In 1952, Alan Turing created a model in which he explained in a simple way pattern formation in one dimension. It was an idealization, however, his explanation worked very well. He established that, surprsingly, patterns are a consequence of the phenomenon of reaction-diffusion. It is a combination between chemical reactions and spreading of these substances. In most cases, this model produces the homogenization of the system, which means that there is the same level of a certain substance everywhere. But, a non-equilibrium instability gives rise to pattern formation.
James D. Murray extended Turing's model to two dimensions. He obtained that with the same model, the type of pattern depends on the shape of the two dimensional surface. The cheetah's body has spots while the cheetah's tail has stripes. This is because the tail is like an elongated rectangle while the body is a wider one. In terrestrial animals the melanin is the responsible of the skin pigmentation. Solving Turing´s equations and changing the two-dimensional shape, you can obtain different types of patterns.
The previous image was obtained from a numerical solution following Murray's ideas. Both images are a recreation of a rectangular shape, but the first one is narrower than the second. Finally, Complex Systems allow us to understand animal patterns. Isn’t that amazing?
If you want to practice on the contents of this page, in the games section there is one related to this topic.