FRACTALS


What are Fractals?
Simply put, fractals can be defined as processes or images that display self-similarity. This basically means that smaller versions of the fractal can be seen throughout the whole fractal. The word "fractal" was actually coined from the concept of a "fractional dimension." Mandelbrot was in the process of publishing a book on his shapes, dimensions, and geometry, when he decided that he needed a name to appropriately describe them. He came across the Latin adjective fractus, from the verb frangere, to break. From this, Mandelbrot created the word fractal (Gleick, 98)

The History of Fractals
Benoit B Mandelbrot a.k.a. "the father of fractals" was the first to investigate the relationship between fractals and nature. He showed that fractals existed in nature and "could accurately model some phenomenon" (Turvey, The Beginnings ,1997). He later introduced several new types of fractals that modeled more complex shapes in narture, including trees and mountains. For example, the pattern of branches sprouting outwards from larger branches that are also extensions of an even larger branch is illustrated in fractals.

Properties of Fractals
John Sheu lists the following three traits of fractals:
-Self-similarity is a defining property of a fractal, which means that a shape cannot be considered a fractal if it does not display this property. This property is best illustrated by Sierpinski's Triangle, which is composed of an infinite number of smaller Sierpinsky's Triangles.
- Infinite Detail, unlike self-similarity, is not a defining property of a fractal. However, it is a trait commonly found in fractals.
-Fractional Dimension literally refers to a fractional dimension. From previous applications in math, we are aware that "1 dimensional" refers to lines. "2 dimensional" refers to shapes that have both length and width, "3 dimensional" refers to objects that have length, width, and depth, and "0 dimensional' refers to a single point. Fractals do not fall in one particular category, and therefore have a fractional dimension. For example, Sierpenski's Triangle begins as a solid triangle with two dimensions. Then, a triangle is removed from the middle, so on and so forth to infinity. Since you are removing from the triangle, you are decreasing the dimension. The shape you began with was two dimensional, but you will never decrease it to one dimensional because it is nowhere close to becoming a line. Thus, the dimension is somewhere between 1 and 2. The approximate dimension is 1.5850. ( Fractional Dimension , 1997)

So, What Are Fractals Used For?
Fine Arts- Fractals can be used to model pre-exsisting music such as Elvis, or can be used to create original composition. They can also be used to create scenes such as landscapes.
Medicine/Biology- Fractals can be used to model our kidneys and nervous system. Our system of veins and arteries are also similar in pattern to that of fractals.
Stock Market- The trends of the Market can display self-similarity in certain points, therfore, fractalscan come into play in economics.
Geography- Even coastlines and mountains can be properly described by fractals such as Koch's curve.
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