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Fractal

A fractal is a geometric shape, which, when mathematically 'magnified', re-reveals itself as constituent to and constructive of its own geometry in a repeating pattern. Fractals are often described as self-similar. A common example given to illustrate this is that of a line and a circle. Given a circle, when one draws closer and closer to the perimeter, or takes successively smaller segments of its circumference and scales them up - thereby magnifying or 'getting closer' to the circumferential line forming the circle - this magnified segment of the closed curve of the circle begins to look like, or converges on, a line. Such a shape, which does not repeat itself when portions of it are magnified, is not a fractal. A line, on the other hand, is still a line no matter how 'close' to it you get - no matter how much you take an interval of the line and upscale it. A line is therefore perhaps the simplest form of fractal.

There are many fractal patterns in nature, and numerous aesthetically appealing and visually intriguing fractals have been discovered by mathematicians and computer scientists. These fractals usually carry the name of their respective discoverers. Famous examples include the Koch curve and Koch Snowflake, the Seirpinski triangle, the Seirpinski sieve or gasket, the Mandelbrot set and its algorithmic sister the Julia set, Lyaponuv sets, and Hilbert curves - among many others. Many fractals discovered with the help of computers, such as the Mandelbrot and Julia sets, are defined iteratively and recursively, but recursiveness is not a requisite for a shape to be fractal. There are many ways for fractals to be self-similar.

Editor(s): B. Long

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