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Abstract
Fractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to the fractal in question, and one can formulate classical and quantum physics within the fractal set. In particular, fractals in space-time can be generated by means of homogeneous spaces associated with appropriate Lie groups. The construction is illustrated by explicit examples.
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Authors (3)
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Diederik Aerts
- Vrije Universiteit Brussel CLEA
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- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.chaos.2015.12.004
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
CHAOS SOLITONS & FRACTALS
no. 83,
pages 201 - 211,
ISSN: 0960-0779 - Language:
- English
- Publication year:
- 2016
- Bibliographic description:
- Aerts D., Czachor M., Kuna M.: Crystallization of space: Space-time fractals from fractal arithmetic// CHAOS SOLITONS & FRACTALS. -Vol. 83, (2016), s.201-211
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.chaos.2015.12.004
- Verified by:
- Gdańsk University of Technology
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