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I created these images using "Flarium24," an excellent program for generating fractal images. You can obtain this program, among other image generating programs, at Iterations et Flarium24. See the "Fractal Links" section below for more related resources. Click on the thumbnail to enlarge the picture.
Note: The following images are sized at 800 x 600 pixels. This makes them appropriate for wallpaper for many computers, but a little slow to download. Also, you may not be able to see the entire image in the frame. However, especially with fractals, reducing the image in size will also reduce the detail of the image if it is later enlarged. I think it is worth the trouble to save the image and view it in a good image program (like Paint Shop Pro), or convert it to a BMP file and set it as wallpaper.
Images Updated June 28, 2004
Chicago recently achieved some praise for its "Cows on Parade" display, which consisted of hundreds of life-size, fiberglass cows rendered by different artists, scattered throughout the downtown area of the city. Other cities have since copied this popular exhibition, with cows and other animals. In tribute to the originality and popularity of the exhibition, here is my contribution, a fractal that turned out to resemble a cow's head.
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Fractals are the result of running certain mathematical equations. The first time the equation is run, there is a "result." However, instead of stopping there, the mathetician cycles the resulting value back into the equation, where it is run, or "iterated," many times. The graph of a complex equation will display apparently "chaotic," or disorderly, behavior. However, when an equation has been iterated a number of times, some elements of order will emerge in the disorder. The images on this page are the result of such mathematical processes.
The above image is the famous "Mandelbrot Set," an image representing the following equation: "The set of all complex c such that iterating z -> z2 + c does not go to infinity." The black area in the image's interior represents those values that, when put into the equation, decay to zero (or "reach a steady state"). The empty area outside the image represents those values that tend to increase to infinity. The colorful "boundary" between these areas represents those values that either oscillate among a number of states ("periodicity") or that exhibit no discernable pattern ("chaos").
Fractals display a characteristic known as "self-similarity." This means that features visible on one scale are repeated, or almost repeated, on a smaller scale. This is shown on the following image, which shows the original Mandelbrot Set, and then focuses on a smaller, similar part of the image.
