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Search results for: fractals

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  • Crystallization of space: Space-time fractals from fractal arithmetic

    Publication

    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...

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  • CHAOS SOLITONS & FRACTALS

    Journals

    ISSN: 0960-0779 , eISSN: 1873-2887

  • Simple Fractal Calculus from Fractal Arithmetic

    Publication

    - REPORTS ON MATHEMATICAL PHYSICS - Year 2018

    Non-Newtonian calculus that starts with elementary non-Diophantine arithmetic operations of a Burgin type is applicable to all fractals whose cardinality is continuum. The resulting definitions of derivatives and integrals are simpler from what one finds in the more traditional literature of the subject, and they often work in the cases where the standard methods fail. As an illustration, we perform a Fourier transform of a real-valued...

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  • Waves Along Fractal Coastlines: From Fractal Arithmetic to Wave Equations

    Publication

    Beginning with addition and multiplication intrinsic to a Koch-type curve, we formulate and solve wave equation describing wave propagation along a fractal coastline. As opposed to examples known from the literature, we do not replace the fractal by the continuum in which it is embedded. This seems to be the first example of a truly intrinsic description of wave propagation along a fractal curve. The theory is relativistically...

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  • Chaos, Solitons and Fractals: X

    Journals

    ISSN: 2590-0544