Mathematics understand how a delicate network of veins in the wings of dragonflies, and learned to shape its growth.
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Dragonflies are some of the best masters of flight in the whole of nature. Two pairs of large wings are formed by layers of durable and lightweight chitin the rigidity of which is attached a network of tiny vessels (trachea) — as a large, “primary”, filled with hemolymph and small with overgrown clearance. Their structure corresponds to the General concept, although the details of branching of the smaller veins strahinich wings are as unique as our fingerprints.
In his recent work a mathematician from Harvard University Chris Rycroft (Chris Rycroft) and his colleagues studied the wings 232 of the members of the order of dragonflies (Odonata) and showed that the complex geometric pattern of veins in their wings formed in the course of a simple four-step process. In an article published in the journal Proceedings of the National Academy of Sciences, the researchers demonstrate how the modeling of all four steps allows to obtain exactly the same patterns.
Top four step of forming a network of veins in the wing of a dragonfly. Bottom left — wing of the present pattern; to the right is the result of computer simulation of all four steps. As you can see, they do not distinguish. / ©Hoffmann et al., 2018
In the first phase the large primary veins grow in predetermined directions, dividing the wing into several large areas. Each of them is many uniformly distributed “centers of growth inhibition” — in this wing such a role can play a cell or group of cells secreting substances that prevent the development of small blood vessels in their direction.
At the next stage each of these “centers” becomes a node in the Voronoi mosaic — such a partitioning of the plane that each “tile” any point is closer to him than to any of the nearby “Mall”. The edges of this mosaic sprout small secondary veins. Finally, the wing grows to a length of the pulling elements of the mosaic.
Interestingly, setting the dimensions, geometry and other characteristics of the wings, scientists have successfully used this algorithm to simulate the network of veins not only dragonflies, but also quite distant from them kinds, including grasshoppers. However, while it refers only to mathematical models of real biological process: scientists have yet to show that he is realized in nature, and figure out which cells and signaling substances are behind this.