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Crystallization of space: Space-time fractals from fractal arithmetic

Author

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  • Aerts, Diederik
  • Czachor, Marek
  • Kuna, Maciej

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 arithmetic 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.

Suggested Citation

  • Aerts, Diederik & Czachor, Marek & Kuna, Maciej, 2016. "Crystallization of space: Space-time fractals from fractal arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 201-211.
    • Handle: RePEc:eee:chsofr:v:83:y:2016:i:c:p:201-211
    DOI: 10.1016/j.chaos.2015.12.004
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    References listed on IDEAS

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    1. Ghosh, Subir, 2014. "Spontaneous generation of a crystalline ground state in a higher derivative theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 245-251.
    2. Pietronero, L., 1987. "The fractal structure of the universe: Correlations of galaxies and clusters and the average mass density," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 144(2), pages 257-284.
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    Cited by:

    1. Aerts, Diederik & Czachor, Marek & Kuna, Maciej, 2016. "Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 461-468.

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    Keywords

    Fractals; Arithmetic; Space-time;
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