Fractals: The Organization of Chaos :: Mathematics Geometry Essays

Fractals The Organization of ChaosPlease ignore the references to pictures or figures. I no longer shake up them, so I could not implicate them on this p maturate. Thanks. Fractals are a relatively new concept in geometry. Most concepts for euclidean geomtery, the comp angiotensin-converting enzyment part of geometry which deals with lines, circles, triangles, and other standard bring into creations, stem from the belated 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 annotate in the preface for The Science of Fractal Images, Computer graphics has played an immanent role both in its development and rapidly growing popularity (V). out front this, mathematicians could only visualize what they were discussing (Mandelbrot, Fractals Form, Chance, and Dimension 2). But now, fractals are the mathematicians answer to nuthouse and therefore can be used to help scientists better apprehend nuature and the universe. Scientists can define any 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 key figure behind the examine of this new science. A Professor of mathematical Sciences at Yale and an IBM Fellow, Mandelbrot is the man who coined the terminal fractal in 1975. Mathematicians, such as Gaston Julia, only defined them as sets in advance this and could only give properties of these sets. Also, there was no way for these early fractal researchers to run into what they were hypothesizing about. As Mandelbrot states in The Fractal Geometry of Nature, I coined fractal from the Latin adjective fractus. The corresponding Latin verb frangere means to break... (4). Mandelbrot used this particular root because of how h e defines fractals. Unlike Euclidean geometry, which has its figures in a particular attribute (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 encyclopaedia a natural fractal of fractal dimension 2.8 ... would be a spongelike shape that is nearly three 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).