Fractals: The Organization of Chaos :: Mathematics Geometry Essays

Fractals The Organization of ChaosPlease ignore the references to pictures or figures. I no longer waste them, so I could non include them on this page. Thanks. Fractals are a relatively new concept in geometry. Most concepts for Euclidean geomtery, the division of geometry which deals with lines, circles, triangles, and other standard shapes, stem from the recent Greek and Early Rioman times. Considering the age of mathematics, the study of fractals is new becasue it dates to the beginning of this century. However, the age of computers brought about an explosion into this yet untamed universe of math. As Heinz-Otto Peitgen and Dietmar Saupe remark in the preface for The Science of Fractal Images, Computer graphics has played an essential role both in its development and rapidly growing popularity (V). Before this, mathematicians could only project what they were discussing (Mandelbrot, Fractals Form, Chance, and Dimension 2). But now, fractals are the mathematicians answer to ch aos and therefore can be used to help scientists better understand nuature and the universe. Scientists can define both structure from a snowflake to a mountain or even an entire planet with this new division in Mathematics. Thus, fractals define our universe. Benoit B. Mandelbrot is a primordial figure behind the rise of this new science. A Professor of mathematical Sciences at Yale and an IBM Fellow, Mandelbrot is the man who coined the term fractal in 1975. Mathematicians, such as Gaston Julia, only specify them as sets before this and could only give properties of these sets. Also, there was no way for these early fractal researchers to see what they were hypothesizing about. As Mandelbrot states in The Fractal Geometry of Nature, I coined fractal from the Latin adjective fractus. The match Latin verb frangere means to break... (4). Mandelbrot used this particular root because of how he defines fractals. Unlike Euclidean geometry, which has its figures in a particular dimens ion (e.g. a square is two-dimensional), fractals have fractional dimensions. They do not exist in just one dimension but can encompass part of another. For example, as Mort La Brecque states in his article on fractals in the Academic American Encyclopedia a natural fractal of fractal dimension 2.8 ... would be a spongelike shape that is nearly collar dimensional in its appearance. A natural fractal of fractal dimension 2.2 would be a much smoother object that just misses being flat (105-106, Mandelbrot Fractals).