Essay on the Art of Chaos :: Exploratory Essays Research Papers

The Art of Chaos Abstract:Â   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.