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The gallery comprises images given by a variety of techniques based on advanced ideas in college mathematics. The images are classified into three |
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The gallery comprises images given by a variety of techniques based on advanced ideas in college mathematics. The images are classified into three |
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§ 1.
Fractal Mountains and Forests
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| The mountains appear realistic as its height function is nowhere differentiable and the terrain shows a typical fractal structure. |
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| The mountains are smooth as the height function is everywhere differentiable. Since every small neighborhood of a point on the surface resembles the tangent plane at the point, the smooth mountains are not a fractal. This is the only non-fractal shown in this section. |
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| This image technically lies somewhere between the preceding two examples as the height function is mostly smooth but still has infinitely many sharp points. Stories About Fractal Plotting shows how to plot this type of fractals. |
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| Only a computer can show a realistic island without birds. |
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| Yes, only a computer can build perfectly symmetric rocks. |
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| No, a computer cannot create a flock of geese like mountains. |
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Top of the Page
Fractal Home
The Mandelbrot Set
Logistic Equation, Etc
Julia Sets
Newton Fractals
Fractal Mountains and Forests
Fantasy Landscapes
Fractals on Nonplanar Surfaces
or Return to the