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Introduction of Fractal

A fractal is a mathematical set which has a fractal dimension which usually exceeds its topological dimension and might fall between the integers. The Fractals are generally self-similar patterns, self-similar means that they are "the same from near as from far".

The Fractals might be precisely similar at every scale or they may be nearly similar at different scales. Description of fractal goes beyond self-similarity per se to exclude the trivial self-similarity and include the idea of a detailed pattern repeating itself.

As mathematical equations, fractals are commonly now here distinguishable, which means that they cannot be measured in traditional manner. An infinite fractal curve can be perceived of as winding through space in a different way from an ordinary line still being a 1-dimensional line yet having a fractal dimension representing it also resemble a surface.

The word "fractal" frequently has different connotations for lay people than mathematicians where the layperson is more likely to be well-known with fractal art than a mathematical conception. The perception of mathematics is difficult to officially define even for mathematicians, but the main features can be understood with little mathematical background.

The feature of "self-similarity", for illustration, is easily understood by analogy to zooming in with a lens or other device which zooms in on digital images to uncover finer formerly invisible new structure. If this is completed on fractals, however, no new detail appears; nothing changes and similar pattern repeats over and over or for some fractals, nearly the similar pattern re-appears again and again. The Self-similarity itself is not essentially counter-intuitive (for illustration people have pondered self-similarity informally like in the infinite regress in parallel mirrors or the homunculus the little man inside the head of the little man inside the head).

 

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