ttempts to graph the capabilities of chaotic equations with computers have produced something amazing, a beautiful form of art called fractals. Fractals areconsidered the face of chaos, as each is a representation of a different non-linear equation. If you were to graph the distance traveled by a free-falling ball at short time intervals, you would get a curve, because the ball is accelerating. While it is not easy tocompute exactly where the ball will be three seconds from now, your curve will tell you with a simple computation. But now, we hit a block. Something so complex, we cannot find a curve to match it. Graph the weather over the past ten years and what do you get A seeminglyrandom set of fluctuations that apparently cannot be represented by an equation. This is chaos. There appears to be no pattern, and the only way to say for surewhere the graph will be in the future is to you have to wait until tomorrow At first glance, fractals seem the same way. They are extremely complex, and they appear to have a random shape. But many fractals are generated through simplemathematical equations. We may be able to use fractals as additional types of equations to which we can map our data. Fractals and Chaos are relatively newbranches of math, since they cannot be explored without powerful computers invented only recently. Without a doubt they have already improved our precision indescribing or classifying "random" or organic things. 9 The most well known of all fractals is the Mandelbrot Set, the Mandelbrot set iterates the equation (z=z^2+c) with z starting at 0 and c varying. Then the Julia Set,which is essentially the same, but z is imaginary and c is real, creating a paradoxical iteration. 10 Part IV: Farewell Chaos scientists hope that by understanding chaos they can accurately predict weather patterns, neutralize tornado-effects, and predict earthquakes. Essentiallypredicting the future to an approximation of possible future...
