Fractal Geometry: Axioms, Fractal Derivative and Its Geometrical Meaning

V. K. Balkhanov (Institute of Physical Materials Science of the Siberian Branch of the Russian Academy of Sciences, Ulan-Ude City, Russia)

Article ID: 475


Physics success is largely determined by using mathematics. Physics often themselves create the necessary mathematical apparatus. This article shows how you can construct a fractal calculus - mathematics of fractal geometry. In modern scientific literature often write from a firm that "there is no strict definition of fractals", to the more moderate that "objects in a certain sense, fractal and similar." We show that fractal geometry is a strict mathematical theory, defined by their axioms. This methodology allows the geometry of axiomatised naturally define fractal integrals and differentials. Consistent application on your input below the axiom gives the opportunity to develop effective methods of measurement of fractal dimension, geometrical interpretation of fractal derivative gain and open dual symmetry.


Fractal geometry; Fractal dimension; Fractal calculus; Duality

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