|
Edited on Wed Aug-27-03 09:57 PM by Prisoner_Number_Six
frac·tal (frâk´tël) n. A geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry. Fractals are used especially in computer modeling of irregular patterns and structures in nature.
Fractals are extensions of traditional Euclidean shapes, such as lines, squares, and circles, with two fundamental properties. First, when you view fractals, you can magnify them an infinite number of times, and they contain structure at every magnification level. Second, you can generate fractals using finite and typically small sets of instructions and data. Fractals grew out of the goal of mathematicians to completely describe the world using standard geometrical expressions. IBM mathematician Benoit B. Mandelbrot, PhD, proved and published the theory behind fractals in 1981 and was the first to view computer-generated fractal structures. The well-known Mandelbrot Set is named in his honor. Another famous fractal researcher, with a set also named for him, is French mathematician Gaston Julia.
===
Okay, now for something you can perhaps understand-- fractals exist on the thin line between order and chaos. Fractals exist in the patterns of smoke, clouds, and flower heads. (The Fibonacci spiral, one of nature's pure geometric forms, appears over and over again in fractal art. The Fibonacci sequence is simple-- 1, 1, 2, 3, 5, 8, 13, etc. Notice you just add the first two numbers to get the next, and so on. It's an infinite spiral. The Fibonacci sequence is represented in the arrangement of seeds in the heads of sunflowers, in snail shells, and so on. It's everywhere in nature.) They are created from mathematical formulae, and they represent almost literally a slice of infinity. Any portion of a true fractal can be magnified infinitely, and you will just end up discovering the same image no matter how far you go down the rabbit hole. It's called "Deep Zooming".
|