Fractal Geometry

Essay by Anonymous UserUniversity, Bachelor'sA-, September 1996

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'Fractal Geometry is not just a chapter of mathematics, but one that

helps Everyman to see the same old world differently'. - Benoit


The world of mathematics usually tends to be thought of as abstract.

Complex and imaginary numbers, real numbers, logarithms, functions, some

tangible and others imperceivable. But these abstract numbers, simply

symbols that conjure an image, a quantity, in our mind, and complex

equations, take on a new meaning with fractals - a concrete one.

Fractals go from being very simple equations on a piece of paper to

colorful, extraordinary images, and most of all, offer an explanation to

things. The importance of fractal geometry is that it provides an

answer, a comprehension, to nature, the world, and the universe.

Fractals occur in swirls of scum on the surface of moving water, the

jagged edges of mountains, ferns, tree trunks, and canyons. They can be

used to model the growth of cities, detail medical procedures and parts

of the human body, create amazing computer graphics, and compress

digital images.

Fractals are about us, and our existence, and they are

present in every mathematical law that governs the universe. Thus,

fractal geometry can be applied to a diverse palette of subjects in

life, and science - the physical, the abstract, and the natural.

We were all astounded by the sudden revelation that the output of a

very simple, two-line generating formula does not have to be a dry and

cold abstraction. When the output was what is now called a fractal,

no one called it artificial... Fractals suddenly broadened the realm

in which understanding can be based on a plain physical basis.

(McGuire, Foreword by Benoit Mandelbrot)

A fractal is a geometric shape that is complex and detailed at every

level of magnification, as well as self-similar.