Self-affine fractal clusters: Conceptual questions and numerical results for directed percolation

B. Hede*, J. Kertész, T. Vicsek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract (may include machine translation)

In this paper we address the question of the existence of a well defined, non-trivial fractal dimension D of self-affine clusters. In spite of the obvious relevance of such clusters to a wide range of phenomena, this problem is still open since the different published predictions for D have not been tested yet. An interesting aspect of the problem is that a nontrivial global dimension for clusters is in contrast with the trivial global dimension of self-affine functions. As a much studied example of self-affine structures, we investigate the infinite directed percolation cluster at the threshold. We measured D in d=2 dimensions by the box counting method. Using a correction to scaling analysis, we obtained D=1.765(10). This result does not agree with any of the proposed relations, but it favors D=1+(1-σν)/σν, where ν and ν are the correlation length exponents and σ is a Fisher exponent in the cluster scaling.

Original languageEnglish
Pages (from-to)829-841
Number of pages13
JournalJournal of Statistical Physics
Volume64
Issue number3-4
DOIs
StatePublished - Aug 1991
Externally publishedYes

Keywords

  • Fractal dimension
  • directed percolation
  • self-affinity

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