There are three common types of plane spirals, the most important of which, as far as fractals are concerned, is the logarithmic spiral. But the most interesting thing, in the context we are dealing with, is that spirals are also the basis of fractals. Even in inanimate nature we discover spirals (many galaxies, for example, are spiral-shaped including ours: The Milky Way). Even the shape of certain organisms can be spiral (such as that of Ammonite, which lived about three hundred million years ago Archimedes drew inspiration from it to even write a treatise: “On Spirals”). The cell nucleus is made up of a long spiral chain, DNA, showing the entire genetic code. Whenever there is a need to expose as much external surface as possible, but at the same time there is a limit to the total volume of available matter, or a disadvantage to weight gain, the evolutionary process favors fractal forms. Returning to nature, we see how, for example, spirals are the basis of the living world. The term fractal was coined in 1975 by Benoît Mandelbrot in the book Les Objets Fractals: Forme, Hasard et Dimension to describe some mathematical behaviors that seemed to have a “chaotic” behavior, and derives from the Latin fractus (broken, broken), as well as the term fraction in fact, fractal images are considered by mathematics to be objects of non-integer dimensionįurthermore, fractals often appear in the study of dynamic systems, in the definition of curves or sets and in chaos theory and are often described recursively by very simple algorithms or equations, written with the help of complex numbers. This feature is often called self-similarity or self-similarity. Fractal geometry is therefore called (non-Euclidean) geometry that studies these structures, recurring for example in engineering network design, in Brownian motion and in galaxies. According to Mandelbrot, the relationships between fractals and nature are deeper than we think.Ī fractal is a geometric object with internal homothety: it is repeated in its form in the same way on different scales, and therefore by enlarging any part of it, a figure similar to the original is obtained. Fractals are also present in nature, as in the geomorphological profile of the mountains, in the clouds, in the ice crystals, in some leaves and flowers. For example, in a tree, especially in the fir, each branch is approximately similar to the whole tree and each branch is in turn similar to its own branch and so on It is also possible to notice phenomena of self-similarity in the shape of a coast: with images taken from satellite gradually larger and larger it can be seen that the general structure of more or less indented gulfs shows many components which, if not identical to the original, however, they look a lot like him. Nature produces many examples of shapes very similar to fractals. Nature has elaborated systems of representation then, which find the maximum perfection and organization in fractals. From the most microscopic organisms to the most beautiful and unlikely manifestations of plants, animals, fungi, etc. This famous phrase by Galileo Galilei finds its fulfillment in the observation of the structures with which nature is composed. Mathematics is the alphabet in which God wrote the universe.
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