Network-growth rule dependence of fractal dimension of percolation cluster on square lattice

Shu Tanaka, Ryo Tamura

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Abstract

To investigate the network-growth rule dependence of certain geometric aspects of percolation clusters, we propose a generalized network-growth rule introducing a generalized parameter q and we study the time evolution of the network. The rule we propose includes a rule in which elements are randomly connected step by step and the rule recently proposed by Achlioptas et al. [Science 323 (2009) 1453]. We consider the q-dependence of the dynamics of the number of elements in the largest cluster. As q increases, the percolation step is delayed. Moreover, we also study the q-dependence of the roughness and the fractal dimension of the percolation cluster.

Original languageEnglish
Article number053002
JournalJournal of the Physical Society of Japan
Volume82
Issue number5
DOIs
Publication statusPublished - 2013 May
Externally publishedYes

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Keywords

  • Achlioptas rule
  • Fractal dimension
  • Network-growth model
  • Percolation
  • Roughness

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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