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Objective: |
In Lesson 1, the Cantor function is applied to a rod that is so thin that we can saw it off without leaving sawdust. Strictly speaking, we assume the rod is a one-dimensional object of the Euclidean world; that is, it has length but no thickness. Here, by extending the Cantor function to the two-dimensional objects of triangle and square, we get the Sierpinski triangle and Cantor gasket, respectively. |
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Further extending to the three-dimensional objects of pyramid and cube, we generate the Sierpinski pyramid and Menger sponge.
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With the aid of programs Prog#5a - 5d, we see how these strange-looking objects are being generated by stepping through iterations of the Cantor function.
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| Scary words: |
Sierpinski triangle and pyramid, Cantor gasket, Menger sponge, Euclidean dimension, tetrahedron.
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Note: Prog#5a - Prog#5d are available for download on the index page. If you use a Macintosh, view the Flash versions. |
