In 1961, the ultra-modern unit of Research Institute of IBM Thomas J. Watson Yorktown red rot of su

It seems that nobody is indifferent to fractals. In fact, many see their first encounter with fractal geometry as a whole new experience, both aesthetically and scientifically Clouds are not spheres ..., mountains are not cones, coastlines are not circles, and tree bark is not smooth. Benoît Mandelbrot, father of fractal geometry.
Today, computer generated fractals can be seen everywhere. Since fractal art articles in the journal Physical serious interest in these unusual structures is increasing. Some of these forms exist only in abstract geometric space, others exist in nature (broccoli, red rot of sugarcane trees, corals) and others are used to model complex phenomena such as cloud formation or operation red rot of sugarcane of the network of capillaries.
In 1961, the ultra-modern unit of Research Institute of IBM Thomas J. Watson Yorktown red rot of sugarcane Heights, NY instructions sent to a printing device Tektronix. This brand conscientious points in unexpected places, and when he stopped chatter, the result looked like a handful of dust scattered on the paper. His Benoit Mandelbrot could not believe. Realize the importance of the event, but what was it exactly? The picture looked like a black and white photo, just out of the bath developer. It was the first glimpse of what was to become red rot of sugarcane a symbol to the world of fractals - Mandelbrot set.
It was the beginning of experimental mathematics, red rot of sugarcane a field near the lab tables and mathematicians, physicists and chemists as. Opens new perspectives. It was a release from the arid sequence theorem definition demonstration. The part that was missing this experimental approach was theoretical foundation behind the images processed. Experimentalists navigate without a map. Mandelbrot coined the word "fractal" - a geometric red rot of sugarcane shape that can be split into parts, so that each is a miniature copy of the whole (Latin fractus meaning "broken", "broken").
What is a fractal, anyway? There is a precise definition, as is normally any mathematical concept? At first, the Mandelbrot did not want such a definition. He would not destroy the magic of this experience, formulating a definition that could be inappropriate or limiting. The concept of fractal, he thought, is like a good wine needs time prior to bottling.
Mandelbrot and his colleagues were no different from ordinary mathematicians. Working with simple formulas. Their idea was based on iteration - repeated application of a formula. The formula that generated the Mandelbrot set is x 2 + c. For certain values of c, string x CEs can generate red rot of sugarcane all sorts of strange things. The Mandelbrot set fractal there is a specific property, that of similarity with themselves. If we look at any part of the crowd Mandelbrot, we see miniature copies of it:
As it happens in science, discoveries are rarely entirely new. Going back to the thread of history, red rot of sugarcane Madelbrot find information about mathematicians such as Henri Poincaré or Arthur Cayley, who questioned fractal hundreds of years before him. Forms discovered the first wave of theorists fractal curves included "wrinkled" and "monster curves." They had not been taken into account before, are considered examples of pathological curves. For this reason, they were locked in the closet mathematics without being analyzed. Curves were rated "smooth", which could be studied using differential calculus. Careers revived the popularity of fractal mathematicians Gaston Julia and Pierre Fatou after WWI. They worked on complex plan structures similar fractals. Obviously, their curves are called fractals and they did not have the appropriate technical equipment to generate such forms. Now, the curves of this type may be computer generated.
Art Fractal (Fractal Art) is an art form that uses fractals and algorithmic representations to generate red rot of sugarcane computer images, animations red rot of sugarcane and music. British artist William Latham fractal red rot of sugarcane geometry used in his works. Greg Sams used fractals to create red rot of sugarcane postcards and t-shirts. Reginald Arkins create fractal art for relaxation. Carlos Ginzburg defined the concept of homo fractalus, centered on the idea that man is the most representative example of a fractal. Spanish architect Xavier Vilalta using fractal geometry to innovate in how to build green buildings.
Koch curve is named after the famous mathematician Niels Fabian red rot of sugarcane Helge von Koch Swedish. Snowflake curve is practically the first fractal. P