Essay on the Art of Chaos

Essay on the Art of Chaos
Abstract: In this paper, I will attempt to explain the nature of Fractals. Both natural and computer generated fractals will be explained. At the end, I hope the reader has a rudimentary sense of fractals in terms of both art and geometry.

Most people live in a state of semi-chaos. Isn?t your cluttered desk an example of the chaos in the world? The words chaos and pattern seem to be a dichotomy, but fractals are both of these things. Basic definitions of fractals include the words self-similar, chaotic, and infinitely complex. Before I go on, let me first define the previous terms in order that the reader will understand their meanings as I will use them.Self-similarity is the idea of an object where there is an apparent pattern in some visual or non-visual way. Sometimes, self-similarity is found with the naked eye, and other times a pattern appears under a microscope, or even when a significant change occurs. The major presumption of self-similarity is some type of pattern.

Chaos has been defined many ways through literature, philosophy, or even daily life. As I stated before, chaos is often used to describe disorder. The way I would like to use it is in terms of a certain unpredictability. Random events or iterations of the same even should cause a chaotic effect. Later, I will show how this is not the case. The last term we need to define is infinitely complex. As the term itself implies, fractals are things that go on forever. Why this is will be discussed later, as well.

In an ideal world, all types of fractals are self-similar, chaotic, and infinitely complex, but in the real world most natural objects are self-similar and chaotic, but not infinitely complex. Some examples of things that are self-similar and chaotic, but not infinitely complex are fern leaves, bronchial tubes, snowflakes, blood vessels, and clouds. Only one example in the world satisfies the three characteristics of a fractal, a coastline.

Coastlines are unique, because the length of a coastline is infinite, but the area within the coastline in finite. The theory of the interaction between infinity and finality is described by a fractal called the Koch Curve. Like coastlines, the length of the shape is infinite, but the area inside of it is finite. The shape of the Koch Curve is a triangle where a triangle one third of the size of the original triangle is placed on the middle of each side of the triangle. Repeated numerous times, the result is an infinitely jagged line.

In recent years, an explosion of fractal images has appeared on the consumer market. The fractals in these cases were generated by a computer; they have the same theory as fractals in nature, but they are greatly more complex. Computer generated fractals are the result of one equation plugged into a computer after iteration. Iteration is the process of feeding the answer from an equation back into itself. Usually, each iteration is assigned a different color, which leads to the ?art? side of fractal technology.

All computer generated fractals met the three requirements of true fractals; they are self-similar, chaotic, and infinitely complex. Self-similarity is expressed in the repeated patterns of design that appear again and again within the same fractal. A chaotic nature is revealed, because the equation used to produce a fractal depends on an imaginary number, therefore, the plotted point is not dependant on anything. Infinite complexity can be easily demonstrated with zoom programs, showing that the deepness of the fractal is infinite.

One of the most complex fractals in the world was discovered by a man named Benoit Mandelbrot. Using the equation z zý + c, where z and c are complex numbers, and c is a constant, the computer produces an infinitely complex, self-similar, and chaotic fractal. If the iteration that resulted from a certain imaginary number went out of control, it was plotted as a number on the screen. If the iteration stayed within the original bounds set, then it was plotted as a black point. Continued again and again with different numbers, a beautiful fractal results.

Debate has recently resulted as people start to claim specific equations and the fractals they create as their own. Copyrights are now created for specific fractals, and copies of the fractal are sold to art and design companies for use on many types of things.

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