The concepts of "fractal geometry" and "fractal" arose in the late 70s, and from the second half of the 80s they firmly entered the dictionary of programmers, mathematicians and even financial traders. The term "fractal" itself comes from the Latin "fractus" and translates as "consisting of fragments." With this word in 1975, the American and French scientist Benoit Mandelbrot outlined the irregular, but self-similar structures that he was engaged in at that time. In 1977, his book was published, which was completely devoted to such a unique and beautiful phenomenon as the fractal geometry of nature.
Benoit Mandelbrot himself was a mathematician, but the term "fractal" does not refer to mathematical concepts. As a rule, it means a geometric figure with one or more of the following properties:
1) with an increase in it, a complex structure is detected;
2) to one degree or another, this figure is similar to itself;
3) it can be built using recursive procedures ;
4) it is characterized by a fractional Hausdorff (fractal) dimension that exceeds the topological one.
Fractal geometry is a real revolution in the mathematical description of nature. With its help, one can describe the world much more clearly than traditional mathematics or physics does. Take, for example, Brownian motion.
It would seem that in the random movement of dust particles suspended in water, complete chaos reigns. Nevertheless, fractal geometry is also present here. Random Brownian motion has a frequency response that can be used to predict phenomena with a large number of statistics. This cannot but be surprising. However, it was the
Brownian motion that helped Mandelbrot in his time to predict price fluctuations in the cost of wool.
Fractal geometry is widely used in computer technology. Just imagine that you need to create a program that can display a three-dimensional model of the coastline, mountains or the edge of the forest. What formulas can all this describe? What features to use? And here fractals come to the rescue. Look at the little twig - it's a tiny little resemblance
big tree. A small cloud is like a big cloud, and a molecule is a tiny analogue of a galaxy. So, using recurrence formulas, that is, those that refer to themselves, you can model quite realistic images.
Fractal geometry finds its application in architecture, the visual arts (fractal impressionism). The sensational paintings of Jackson Pollack are a vivid example of this. With the help of fractals, the film industry made a real breakthrough - before that, the artificial elements of the landscape had never looked so realistic. Economists use them to predict stock price fluctuations. The world of fractals still holds many surprising things, because this is a living language of nature, and who knows what discovery he will push humanity into in the next 5-10 years?