[en] In this paper, we emphasize three different techniques for the growth of fractal trees with a desired fractal dimension D-f. The three different growths are due to the influence of (i) stretched branches, (ii) dead ends, or (iii) a variable branching rate. Several examples are given. We point out that geometrical and physical properties (skeleton dimension, percolation exponents, self-avoiding walk) of fractal tress depend strongly on their type. The most striking result is that the critical exponents at the percolation transition are nonuniversal since they depend on the tree type. The critical exponents depend on D-f for trees of types (ii) and (iii).
Disciplines :
Physics
Author, co-author :
Vandewalle, Nicolas ; Université de Liège - ULiège > Département de physique > Physique statistique
Ausloos, Marcel ; Université de Liège - ULiège > Département de physique > Physique statistique appliquée et des matériaux - S.U.P.R.A.S.
Language :
English
Title :
Construction and properties of fractal trees with tunable dimension: The interplay of geometry and physics
Publication date :
January 1997
Journal title :
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
ISSN :
1063-651X
eISSN :
1095-3787
Publisher :
American Physical Society, United States - Maryland
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