# Birds love and pattern

If you are a bird in estrus, you have to choose the most suitable object for you from among many suitors. The most suitable means the healthiest and most fertile body. Is there any way?
Look at the complexity of the fractal geometric pattern on the suitor’s neck!
Fractal geometry is often used by mathematicians to study complex patterns such as coastlines, plant shapes, and animal patterns. Fractal geometry brings people some new ideas. For example, the dimensions of geometric figures are not necessarily all integers, but also fractions. For example, as we all know, straight lines are 1-dimensional and planes are 2-dimensional, but the dimension of the fractal geometry drawn on the plane is neither 1-dimensional nor 2-dimensional, but is between 1- and 2-dimensional. Moreover, in general, the more complicated the pattern, the higher the dimension.
Recently, a Spanish naturalist wanted to see if studying the pattern of bird feathers with fractal geometry could tell us more useful information.
He studied red-legged quails. He photographed a large number of beautiful patterns around the neck of red-legged quail, and processed them on a computer to calculate the fractal dimension of each pattern. He found that the transition from a monotonous area to a streaky area, the more frequent the change, the higher the dimension of the decoration, indicating that the decoration is more complicated.
In order to see if the dimension of the ornamentation is related to the adaptability of the red-legged quail, he chose 68 quails with almost the same ornamentation dimension and divided them into two groups. They are malnourished. Six months later, he found that the texture dimension of the former group was the same as before the experiment, while the texture dimension of the latter group decreased. After inspection, the immunity of the latter group also decreased.
This shows that the decoration on the neck of a quail can be used as a “living advertisement” for its own health. This tells us not only its own survivability, but also its key to winning the courtship competition.
This conclusion probably applies to many other birds. Of course birds haven’t learned fractal geometry, but the decoration is complicated or not. They can tell at a glance.