Academic Journal
FRACTAL GEOMETRY: HISTORICAL AND CONCEPTUAL BACKGROUND.
| Τίτλος: | FRACTAL GEOMETRY: HISTORICAL AND CONCEPTUAL BACKGROUND. |
|---|---|
| Συγγραφείς: | SAMAYOA-OCHOA, DIDIER1 (AUTHOR) dsamayoa@ipn.mx, GARCIA-OTAMENDI, EDGAR1 (AUTHOR) egarciao0600@egresado.ipn.mx, BALANKIN, ALEXANDER S.1 (AUTHOR) abalankin@ipn.mx |
| Πηγή: | Fractals. 2026, Vol. 34 Issue 9, p1-18. 18p. |
| Θεματικοί όροι: | *Fractals, *Scale invariance (Statistical physics), *Dimensionless numbers, *Systems theory, *Conceptual history, *Symmetry |
| Περίληψη: | Fifty years ago, the term fractal was introduced by Mandelbrot in his book "Les objet fractals: forme, hasard et dimension". Fractal geometry deals with intricate patterns and irregular shapes possessing scale and/or conformal symmetry. Presently, fractal geometry serves as a framework for studies of complex systems of diverse nature. One of the most fundamental geometric conceptions is the concept of symmetry. Different geometries can be classified according to the group of transformations under which their propositions remain true. In particular, the key symmetry of fractal geometry is scale invariance. Another crucial paradigm in fractal geometry is that different properties of a fractal pattern are governed by different dimension numbers, at least one of which differs from the topological dimension. Accordingly, the inherent features of a fractal pattern are characterized by a set of generally independent dimension numbers. These numbers allow us to classify fractal patterns. In this paper, we briefly survey the historical background and conceptual foundations of fractal geometry. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: | Academic Search Index |
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