LYCOS RETRIEVER 
Mandelbrot Set: Program
built 170 days ago
The Mandelbrot set was discovered much later than Julia sets. Julia and Fatou were looking at Julia sets right after World War I, but until computers came along and got easier to program -- in the 1960s and 1970s -- mathematicians didn't know much about what Julia sets looked like and how many different kinds there were. In the 1970s, Benoit Mandelbrot was interested in looking at highly irregular forms in geometry, such as coastlines, mountain range shapes, and coral formations, and looked again at Julia sets with the aid of a computer.
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With the aid of a relatively simple program a computer can be converted into a kind of microscope for viewing the boundary of the Mandelbrot set. In principle one can zoom in for a closer look at any part of the set at any magnification (see Color Plate 1). From a distant vantage the set resembles a squat, wart-covered figure 8 Iying on its side. The inside of the figure is ominously black. Surrounding it is a halo colored electric white, which gives way to deep blues and blacks in the outer reaches of the plane.
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After starting the program the Mandelbrot set appears. You form a small box with the mouse and move it with pressed mouse button to an edge. Then you press the enter key. A new picture appears on the screen. If you want you can look for a new place and press the enter key. The patterns repeat.
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Sometimes, while the Mandelbrot set is being drawn, the program quits with the message "this program has performed an illegal operation" and an " Invalid page fault". This forces shutting down Netscape and starting over.
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Nearly everyone who writes computer programs and is interested in computer graphics has had a try with the Mandelbrot set. It is an unforgettable experience if a simple program produces the complicated Mandelbrot set for the first time. In former times it took hours and hours (Commodore 64 nostalgia!).
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This program will draw the Mandelbrot set in C#. It allows you to zoom in to any measure. It ... supports ColorMaps to style the set. Each ColorMap file has 256 lines, one for each RGB value calculated by the Mandel set.
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