Elementary fractal geometry. New relatives of the Sierpiński gasket

By slight modification of the data of the Sierpiński gasket, keeping the open set condition fulfilled, we obtain self-similar sets with very dense parts, similar to fractals in nature and in random models. This is caused by a complicated structure of the open set and is revealed only under magnifica...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2018-06, Vol.28 (6), p.063104-063104
Main Authors: Bandt, Christoph, Mekhontsev, Dmitry
Format: Article
Language:English
Subjects:
Fractal geometry
Fractal models
Self-similarity
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Summary:By slight modification of the data of the Sierpiński gasket, keeping the open set condition fulfilled, we obtain self-similar sets with very dense parts, similar to fractals in nature and in random models. This is caused by a complicated structure of the open set and is revealed only under magnification. Thus, the family of self-similar sets with separation condition is much richer and has higher modelling potential than usually expected. An interactive computer search for such examples and new properties for their classification are discussed.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.5023890