Fractal geometry is an amazing miracle

The concepts "fractal geometry" and "fractal" arose in the late 70's, and from the second half of the 80s they firmly entered the dictionary of programmers, mathematicians and even financial traders. The very term "fractal" comes from the Latin "fractus" and is translated as "consisting of fragments." This word in 1975, the American and French scientist Benoit Mandelbrot designated the irregular, but self-similar structures that he was at that time engaged in. In 1977 his book was published, which was entirely devoted to such a unique and beautiful phenomenon as the fractal geometry of nature.

Benois Mandelbrot himself was a mathematician, however the term "fractal" does not apply 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 revealed;

2) to some extent this figure is similar to itself;

3) it can be constructed using recursive procedures;

4) it is characterized by a fractional Hausdorff (fractal) dimension exceeding the topological dimension.

Fractal geometry is a real revolution in the mathematical description of nature. With its help, you can describe the world much more clearly than traditional math or physics does. Take, for example, the Brownian movement. It would seem that chaos reigns in the random movement of particles of dust suspended in the water. Nevertheless, fractal geometry is also present here. The disordered Brownian motion has a frequency response that can be used to predict phenomena with a large number of statistical data. This can not but surprise. However, it was the Brownian movement that helped Mandelbrot in its time to predict price fluctuations in the value of wool.

Fractal geometry has found wide application in computer technology. Imagine that you need to create a program that can display a three-dimensional model of the coastline, mountains or forest edges. What formulas can all describe this? What features to use? And here to help come fractals. Look at the small twig - this is a tiny likeness Of a large tree. A small cloud is something like a big cloud, and a molecule is a tiny analog of the galaxy. So, applying recurrent formulas, that is, those that refer to themselves, it is possible to model quite realistic images.

Fractal geometry finds its application in architecture, fine arts (fractal impressionism). Jackson Pollack's paintings, once famous in his time, are a vivid example of this. With the help of fractals, the film industry has made a real breakthrough - before that, the artificial elements of the landscape have never looked so realistic. Economists use them to predict fluctuations in the rates of securities. The world of fractals still contains a lot of surprising, because it is a living language of nature, and who knows what kind of discovery it will push humanity in the next 5-10 years?