Fractals and nonstandard analysis
- 1 May 1984
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 25 (5) , 1296-1300
- https://doi.org/10.1063/1.526285
Abstract
We describe and analyze a parametrization of fractal ‘‘curves’’ (i.e., fractal of topological dimension 1). The nondifferentiability of fractals and their infinite length forbid a complete description based on usual real numbers. We show that using nonstandard analysis it is possible to solve this problem: A class of nonstandard curves (whose standard part is the usual fractal) is defined so that a curvilinear coordinate along the fractal can be built, this being the first step towards the possible definition and study of a fractal space. We mention fields of physics to which such a formalism could be applied in the future.Keywords
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