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

B. Hede, J. Kertész, T. Vicsek

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

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
Publication statusPublished - Aug 1991

Fingerprint

Directed Percolation
Self-affine
Fractal
fractals
Numerical Results
Global Dimension
Exponent
exponents
Affine Structure
scaling
Corrections to Scaling
Affine Function
Correlation Length
Fractal Dimension
boxes
Well-defined
Counting
counting
Trivial
Scaling

Keywords

  • directed percolation
  • Fractal dimension
  • self-affinity

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

Self-affine fractal clusters : Conceptual questions and numerical results for directed percolation. / Hede, B.; Kertész, J.; Vicsek, T.

In: Journal of Statistical Physics, Vol. 64, No. 3-4, 08.1991, p. 829-841.

Research output: Contribution to journalArticle

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