Frakties

Frakties, also known as fractals, are complex geometric shapes that can be split into parts, each of which is a reduced-scale copy of the whole. This property is known as self-similarity. Fractals are characterized by fine structure at arbitrarily small scales and are typically created through iterative processes or recursive definitions.

The term "fractal" was coined by the mathematician Benoit Mandelbrot in 1975, derived from the Latin word "fractus," meaning "broken" or "fractured." Mandelbrot's work brought fractals into the mainstream of mathematical study, although the underlying concepts had been studied by earlier mathematicians such as Gaston Julia and Helge von Koch.

Frakties exhibit several key properties. Self-similarity means that the fractal appears similar at any magnification, revealing more detail as you zoom in. This is in contrast to regular geometric shapes, which become simpler at higher magnifications. Fractals also often have a fractional dimension, which is a measure of their complexity. This dimension is not an integer like the dimensions of familiar shapes (e.g., lines, squares, cubes) but a fraction, hence the name "fractal."

Fractals are found in various natural phenomena, such as the branching of trees, the formation of coastlines, and the structure of clouds. They are also used in computer graphics, data compression, and the modeling of complex systems in physics, biology, and finance. The study of fractals has led to significant advancements in understanding the intricate patterns and structures observed in both nature and human-made systems.