Pregled bibliografske jedinice broj: 941115
Box-counting dimensions of generalised fractal nests
Box-counting dimensions of generalised fractal nests // Chaos, solitons and fractals, 113 (2018), 125-134 doi:10.1016/j.chaos.2018.05.025 (međunarodna recenzija, članak, znanstveni)
CROSBI ID: 941115 Za ispravke kontaktirajte CROSBI podršku putem web obrasca
Naslov
Box-counting dimensions of generalised fractal
nests
Autori
Miličić, Siniša
Izvornik
Chaos, solitons and fractals (0960-0779) 113
(2018);
125-134
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
box-counting dimension, Minkowski-Bouligand dimension, uniform Cantor set, fractal nests, (a, b)-bifractals
Sažetak
Fractal nests are sets defined as unions of unit n-spheres scaled by a sequence of k−α for some α>0. In this article we generalise the concept to subsets of such spheres and find the formulas for their box counting dimensions. We introduce some novel classes of parameterised fractal nests and apply these results to compute the dimensions with respect to these parameters. We also show that these dimensions can be seen numerically. These results motivate further research that may explain the unintuitive behaviour of box counting dimensions for nest-type fractals, and in general the class of sets where the box-counting dimension differs from the Hausdorff dimension.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
Citiraj ovu publikaciju:
Časopis indeksira:
- Current Contents Connect (CCC)
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus
