Fractal geometry - an amazing miracle

concepts of "fractal geometry" and "fractal" emerged in the late 70s., And the second half of the 80s, they have become part of the vocabulary of programmers, mathematicians and even financial traders.The term "fractal" comes from the Latin "fractus" and translates as "consisting of fragments."This word in 1975, the American and French scientist Benoit Mandelbrot outlined irregular but self-similar structure, which at the time he was engaged.In 1977 he published his book, which was entirely devoted to this unique and beautiful phenomenon of fractal geometry of nature.

Sam Benoit Mandelbrot was a mathematician, but the term "fractal" is not a mathematical concepts.As a rule, it means the geometric shape having one or more of the following properties:

1) with an increase in her is found a complex structure;

2) to a greater or lesser extent, this figure is similar to itself;

3) it can be constructed using recursive procedures;

4) it is characterized by fractional Hausdorff (fractal) dimension exceeding topology.

Fractal geometry - a real revolution in the mathematical description of nature.You can use it to describe the world is much more clear than it does traditional math or physics.Take, for example, Brownian motion.It would seem that in a random movement of dust particles suspended in the water, there is complete chaos.Nevertheless, even here there is fractal geometry.The random Brownian motion has a frequency response that can be used to predict events with a large number of statistical data.This can not but cause surprise.However, it is the Brownian motion helped in their time Mandelbrot predict price fluctuations cost of wool.

Fractal geometry has been widely used in computer technology.Just imagine that you need to create a program that can display a three-dimensional model of the coastline, the mountains or the forest edge.What formulas describe all possible?What functions to use?And here to the aid of fractals.Look at the small branch - this tiny semblance of a large tree.A small cloud is a sort of large clouds, and the molecule - a tiny analogue of the galaxy.So, using recurrence formulas, that is, those that refer to themselves, it is possible to simulate very realistic images.

Fractal geometry finds its application in architecture, fine arts (Impressionism fractal).Sensational once Jackson Pollack paintings are a vivid example of this.Using fractals film industry has made a real breakthrough - before artificial features have never looked so realistic.Economists use them to predict market fluctuations.World fractals stores many more surprising, because it is a living language of nature, and who knows to what he will encourage the opening of mankind in the next 5-10 years?