Affiliation:
1. SEPI-ESIME Zacatenco, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos, México City 07738, Mexico
Abstract
The key issues in fractal geometry concern scale invariance (self-similarity or self-affinity) and the notion of a fractal dimension D which exceeds the topological dimension d. In this regard, we point out that the constitutive inequality D>d can have either a geometric or topological origin, or both. The main topological features of fractals are their connectedness, connectivity, ramification, and loopiness. We argue that these features can be specified by six basic dimension numbers which are generally independent from each other. However, for many kinds of fractals, the number of independent dimensions may be reduced due to the peculiarities of specific kinds of fractals. Accordingly, we survey the paradigmatic fractals from a topological perspective. Some challenging points are outlined.
Funder
Instituto Politécnico Nacional Project
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis
Reference234 articles.
1. Husain, A., Nanda, M.N., Chowdary, M.S., and Sajid, M. (2022). Fractals: An Eclectic Survey, Part-I. Fractal Fract., 6.
2. Husain, A., Nanda, M.N., Chowdary, M.S., and Sajid, M. (2022). Fractals: An Eclectic Survey, Part-II. Fractal Fract., 6.
3. Fractional space approach to studies of physical phenomena on fractals and in confined low-dimensional systems;Balankin;Chaos Solitons Fractals,2020
4. Mandelbrot, B.B. (1975). Les Objets Fractals: Forme, Hasard et Dimension, Flammarion.
5. Siegmund-Schultze, R. (1988). Ausgewählte Kapitel aus der Funktionenlehre. Teubner-Archiv zur Mathematik, Springer.
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