Mathematicians understood how an openwork network of veins is formed in the wings of dragonflies and learned to model its growth.
Dragonflies are some of the best flight masters in all wildlife. Two pairs of their large wings are formed by layers of strong and light chitin, the rigidity of which is given by a network of tiny vessels (trachea) - both large, "primary" filled with hemolymph, and small with an overgrown lumen. Their structure obeys a general schematic diagram, although the details of the branching of small veins of dragonfly wings are as unique as our fingerprints.
In recent work, Harvard mathematician Chris Rycroft and his colleagues examined the wings of 232 members of the order of dragonflies (Odonata) and showed that the complex geometric pattern of veins in their wings is formed in a simple four-step process. In an article published in the journal Proceedings of the National Academy of Sciences, scientists demonstrate how modeling all four steps produces exactly the same patterns.
Above - four steps in the formation of a network of veins in the wing of a dragonfly. At the bottom left is the pattern of a real wing; on the right - the result of computer simulation of all four steps. As you can see, they cannot be distinguished. / © Hoffmann et al., 2018
At the first stage, large primary veins sprout in predetermined directions, dividing the wing into several large sections. In each of them, many evenly distributed "centers of growth inhibition" are distinguished - in a real wing, such a role can be played by cells or groups of cells that secrete substances that prevent the development of small vessels in their direction.
At the next stage, each of these "centers" becomes a node of the Voronoi mosaic - such a division of the plane that in each "tile" any point is closer to it than to any neighboring "center". Small secondary veins grow along the edges of this mosaic. Finally, the wing grows in length, pulling out the mosaic elements.
Interestingly, by setting the size, geometry and other characteristics of the wings, scientists have successfully used such an algorithm to accurately model the network of veins not only of dragonflies, but also of species quite distant from them, including grasshoppers. However, so far we are only talking about a mathematical model of a real biological process: scientists have yet to show that this is how it is realized in nature, and find out what cells and signaling substances are behind this.