- Complex Numbers
- The Mandelbrot Set
- Color and the Mandelbrot Set
- Generating the Mandelbrot Set
- The Demo Program
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Color and the Mandelbrot Set
Some reproductions of the Mandelbrot set are very colorful. This effect is achieved by making use of the iterative nature of the calculations. Each point outside the set is assigned a color based on how many iterations it took to determine that the point was, in fact, outside the set. Points that are relatively far from the set will take only one iteration; the closer you get to the edge of the set, the more iterations it takes. The set itself remains black—it’s the region around the set that displays the colors (see Figure 3).
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Figure 3 The Mandelbrot set displayed with colors.
When you use colors and zoom in on a part of the set, you get some really spectacular images, as shown in Figure 4.
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Figure 4 Zooming on the details of the Mandelbrot set.