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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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  • 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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  • CHAOS SOLITONS & FRACTALS

    Journals

    ISSN: 0960-0779 , eISSN: 1873-2887

  • 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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  • Uniwersytet przyszłości organizacją fraktalną?

    Publication

    - Year 2006

    Autor proponuje wdrożenie idei organizacji fraktalnej do realiów uniwersytetu, w celu ograniczenia znaczenia barier kulturowych i organizacyjnych i przekształcenia uczelni w kierunku elastycznej organizacji. Takie cechy organizacji fraktalnej jak samoorganizacja, samopodobieństwo, witalność, dynamika i nawigowanie odniesiono do realiów współczenej uczelni wskazując ich znaczenie dla wsparcia rozwoju uczelni w społeczeństwie wiedzy....