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Benoit Mandelbrot (1924-2010) was a Polish mathematician who worked at Yale University (United States) in the development of a new branch of mathematics. He was a visionary who laid the foundations for what we now know as fractals.
Today we do not have a universally accepted definition of what a fractal is, although it is true that most authors link this term with some form of self-similarity -also called self-similarity- related to fractional dimensions.
The classic example that is usually put of a fractal is that of Romanesco broccoli. Each small portion of this vegetable reproduces its global form. And it is that another of the intrinsic characteristics of fractals are the iterations that consist of repeating the same figure ‘n’ times.
In a way, it could be said that fractals move in the blurred border that separates mathematics, art and beauty.
in our body
In our organism we also find fractals. The bloodstream may seem like chaos, but there is neither randomness nor anarchy in it. Metaphorically, the circulatory system is a network of roads, in which the highways give way to smaller roads until they reach the regional ones. Through this complex network, blood flows to reach all corners of our body.
In this way, and under normal conditions, it is capable of covering an area of about 100,000 kilometers without any traffic jams. To do this, it has to manage a complex polynomial in which blood pressure, the amount of blood received by each of the branches, the circadian rhythm, the cardiac cycle, breathing, etc., participate.
We also find fractals in our respiratory tree, which is made up of a complex network of tubes through which air circulates. The trachea branches into bronchi, these, in turn, into bronchioles, which end up oxygenating more than three hundred million alveoli, which form a structure quite similar to a tree.
It has been estimated that, under normal conditions, our lungs have a surface area similar to half a tennis court. The efficiency of gas exchange at the level of the alveoli is directly proportional to the surface of the alveoli.
ocean depths
Mandelbrot went a step further by analyzing the movements made by animals with the perspective of fractals. He discovered that there is a movement, which is currently known as ‘Levy’s flight’, and that it consists of alternating short movements at random -Brownian- with others with longer trajectories.
This type of movement is the one presented, among other animals, by sharks. Scientists have observed that these marine predators follow mathematical strategies in the efficient search for their prey. And it is that, in addition to making stochastic movements in any direction, in certain situations, such as when food is scarce or when there are other competitors, these movements are replaced by others that consist of making long trajectories followed by short movements. With this alternative pattern, the sharks manage to optimize the success of the hunt.
We also find these types of patterns in social networks, specifically in the structure of contacts and the creation of weak links. Somehow in our social networks we alternate contacts closer to us (friends, co-workers, relatives…) with other ties that we could call weak and that are formed by those people far from that cluster but who, in some way, open us up. the window to other possibilities. Levy’s flights are the geometric drawing of some phenomena that spread through social networks.
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