Ocenjevanje fraktalnosti prostorskovpetih kompleksnih mrež

magistrsko delo

David Jesenko (Author), Borut Žalik (Mentor), Domen Mongus (Co-mentor)

Abstract

V magistrskem delu opišemo dve zelo zanimivi področji računalništva, kompleksne mreže in fraktale. S kompleksnimi mrežami lahko na preprost in enostaven način predstavimo sestavljene in težko opisljive strukture. Vozlišča v našem primeru predstavljajo objekte v prostoru, povezave med njimi pa interakcije. Zato govorimo o prostorskovpetih mrežah. Drugi del magistrskega dela predstavljajo fraktali, ki s svojo lastnostjo samopodobnosti vzbujajo veliko pozornosti v svetu računalništva. Dejanske fraktale je težko opisati in prepoznati, eden od načinov pa je s pomočjo fraktalne dimenzije. S fraktalno dimenzijo lahko opišemo kakršnekoli fraktale, dimenzija pa je značilno manjša od prostora, v katerega so vpeti. V tem magistrskem delu predstavimo postopek ocenjevanja fraktalnosti mrež. Razvita metoda temelji na štetju zasedenih škatelj. Z rezultati pokažemo njeno učinkovitost pri razpoznavi fraktalnih struktur, skritih v prostorskovpetih mrežah.

Keywords

kompleksni sistemi;kompleksne mreže;fraktali;fraktalna dimenzija;ocenjevanje fraktalnosti;algoritmi;

Data

Language:	Slovenian
Year of publishing:	2014
Typology:	2.09 - Master's Thesis
Organization:	UM FERI - Faculty of Electrical Engineering and Computer Science
Publisher:	[D. Jesenko]
UDC:	004.421:530.191(043.2)
COBISS:	18055446
Views:	1492
Downloads:	134
Average score:	0 (0 votes)
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Other data

Secondary language:	English
Secondary title:	SPATIALLY - EMBEDDED COMPLEX NETWORK ESTIMATION USING FRACTAL DIMENSION
Secondary abstract:	In this thesis we describe two very interesting areas of computer science: complex networks and fractals. With the complex networks we can, in an easy and simple manner, present composite structures and structures that are difficult to describe. In our case, the nodes present the objects in space, while the connections between them present interactions. We talk about spatially embedded networks. The second part of the thesis consider fractals, which with their characteristic of self-similarity raise a lot of attention in the world of computer science. The actual fractals are difficult to describe and to recognize, one of the ways to do so is with the help of fractal dimension. With the fractal dimension we can describe any kinds of fractals and the dimension is smaller than the space in which they are embedded. With the implementation of the box-counting algorithm we have assessed the fractality of the spatially embedded networks. We show that spatially embedded networks have fractal properties.
Secondary keywords:	complex systems;complex networks;fractals;fractal dimension;estimation of fractal dimension;algorithms;
URN:	URN:SI:UM:
Type (COBISS):	Master's thesis/paper
Thesis comment:	Univ. v Mariboru, Fak. za elektrotehniko, računalništvo in informatiko
Pages:	XI, 42 f.
ID:	8730057