An Introduction to Fractal Geometry

An Introduction to Fractal Geometry

Document details
Category: Mathematics Essay
Subcategory: Geometry
Words: 1497
Pages: 7

Fractal Geometry"Fractal Geometry is not just a chapter of mathematics, but one that helpsEveryman to see the same old world differently". - Benoit MandelbrotThe world of mathematics usually tends to be thought of as abstract. Complex andimaginary numbers, real numbers, logarithms, functions, some tangible and othersimperceivable. But these abstract numbers, simply symbols that conjure an image,a quantity, in our mind, and complex equations, take on a new meaning withfractals - a concrete one. Fractals go from being very simple equations on apiece of paper to colorful, extraordinary images, and most of all, offer anexplanation to things. The importance of fractal geometry is that it provides ananswer, a comprehension, to nature, the world, and the universe. Fractals occurin 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 computergraphics, 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, andscience - 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 ofmagnification, as well as self-similar. Self-similarity is something looking thesame over all ranges of scale, meaning a small portion...

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