Fractal
Fractal
A Fractal (/ˈfræk.təl/; from Latin fractus, "broken") is a complex geometric shape that can be split into parts, each of which is a reduced-scale copy of the whole. Fractals are self-similar, meaning they are "scale invariant". This property of self-similarity applies to the whole fractal and to its parts, no matter how small.
Etymology
The term "fractal" was first used by mathematician Benoit Mandelbrot in 1975. He derived it from the Latin word fractus, meaning "broken" or "fractured". A fractal is a shape that is "broken" into parts, each of which is a reduced-scale copy of the whole.
Properties
Fractals have two key properties: self-similarity and scale invariance.
- Self-similarity: This means that a fractal appears the same at any scale. If you zoom in on a part of a fractal, the smaller portion will look the same as the whole fractal.
- Scale invariance: This means that the fractal has the same characteristics regardless of the scale at which it is viewed.
Examples
Examples of fractals include the Mandelbrot set, the Julia set, and the Sierpinski triangle. These are mathematical constructs, but fractals can also be found in nature. For example, the branching patterns of trees and rivers, the shape of coastlines, and the structure of snowflakes are all fractal in nature.
Applications
Fractals have many practical applications in various fields such as computer graphics, physics, data compression, and chaos theory. They are used in computer modeling of natural structures, in image compression algorithms, and in the study of fluid dynamics, among other things.
Related Terms
External links
- Medical encyclopedia article on Fractal
- Wikipedia's article - Fractal
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