IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v83y2016icp201-211.html
   My bibliography  Save this article

Crystallization of space: Space-time fractals from fractal arithmetic

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077915004221
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2015.12.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dickau, Jonathan J., 2009. "Fractal cosmology," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2103-2105.
    2. Puetz, Stephen J. & Prokoph, Andreas & Borchardt, Glenn & Mason, Edward W., 2014. "Evidence of synchronous, decadal to billion year cycles in geological, genetic, and astronomical events," Chaos, Solitons & Fractals, Elsevier, vol. 62, pages 55-75.
    3. Momin Mukherjee, 2017. "A Review of Research Design," Post-Print hal-01592483, HAL.
    4. Kantelhardt, Jan W & Eduardo Roman, H & Greiner, Martin, 1995. "Discrete wavelet approach to multifractality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 220(3), pages 219-238.
    5. Puetz, Stephen J., 2022. "The infinitely fractal universe paradigm and consupponibility," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    6. Calabrese, Armando & Capece, Guendalina & Costa, Roberta & Di Pillo, Francesca & Giuffrida, Stefania, 2018. "A ‘power law’ based method to reduce size-related bias in indicators of knowledge performance: An application to university research assessment," Journal of Informetrics, Elsevier, vol. 12(4), pages 1263-1281.
    7. Vlad, Marcel Ovidiu, 1994. "Non-Markovian approach for anomalous diffusion with infinite memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 208(2), pages 167-176.

    More about this item

    Keywords

    Fractals; Arithmetic; Space-time;
    All these keywords.

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:83:y:2016:i:c:p:201-211. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.