Mandelbrot set + symmetry groups \(\ast \) higher dimensions = ? (Q1930536)
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scientific article; zbMATH DE number 6124641
| Language | Label | Description | Also known as |
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| English | Mandelbrot set + symmetry groups \(\ast \) higher dimensions = ? |
scientific article; zbMATH DE number 6124641 |
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Mandelbrot set + symmetry groups \(\ast \) higher dimensions = ? (English)
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11 January 2013
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The author constructs higher-dimensional analogs of the Mandelbrot set. These analogs are referred to as MandalaBeth sets. By construction, these sets are invariant under the action of certain symmetry groups. It is shown that the generating function of a MandalaBeth set is the sum (over the symmetry group) of conjugates (by isometries) of the generating functions of the Mandelbrot set. Numerous pictures of three-dimensional and projections of four-dimensional MandalaBeth fractals are shown.
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MandalaBeth
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Mandelbrot set
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symmetry groups
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higher dimensions
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fractals
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