Network-Growth Rule Dependence of Fractal Dimension of Percolation Cluster on Square Lattice
arXiv:1111.2005 · doi:10.7566/JPSJ.82.053002
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 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 {\it et al.} [Science {\bf 323} (2009) 1453]. We consider the -dependence of the dynamics of the number of elements in the largest cluster. As increases, the percolation step is delayed. Moreover, we also study the -dependence of the roughness and the fractal dimension of the percolation cluster.
4 pages, 5 figures, accepted for publication in Journal of the Physical Society of Japan
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