TY - JOUR
T1 - A Brief Survey of Paradigmatic Fractals from a Topological Perspective
AU - Patiño Ortiz, Julián
AU - Patiño Ortiz, Miguel
AU - Martínez-Cruz, Miguel Ángel
AU - Balankin, Alexander S.
N1 - Publisher Copyright:
© 2023 by the authors.
PY - 2023/8
Y1 - 2023/8
N2 - The key issues in fractal geometry concern scale invariance (self-similarity or self-affinity) and the notion of a fractal dimension (Formula presented.) which exceeds the topological dimension (Formula presented.). In this regard, we point out that the constitutive inequality (Formula presented.) 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.
AB - The key issues in fractal geometry concern scale invariance (self-similarity or self-affinity) and the notion of a fractal dimension (Formula presented.) which exceeds the topological dimension (Formula presented.). In this regard, we point out that the constitutive inequality (Formula presented.) 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.
KW - connectedness
KW - connectivity
KW - degrees of freedom
KW - dimension numbers
KW - loopiness
KW - ramification
KW - Fractal
KW - connectedness
KW - degrees of freedom
KW - Loopiness
KW - Ramification
KW - connectivity
UR - http://www.scopus.com/inward/record.url?scp=85168996166&partnerID=8YFLogxK
U2 - 10.3390/fractalfract7080597
DO - 10.3390/fractalfract7080597
M3 - Artículo de revisión
AN - SCOPUS:85168996166
SN - 2504-3110
VL - 7
JO - Fractal and Fractional
JF - Fractal and Fractional
IS - 8
M1 - 597
ER -