CONSTRUCTION AND PROPERTIES OF FRACTAL TREES WITH TUNABLE DIMENSION -THE INTERPLAY OF GEOMETRY AND PHYSICS

In this paper, we emphasize three different techniques for the growth of fractal trees with a desired fractal dimension D-f. The three diffe rent growths are due to the influence of (i) stretched branches, (ii) dead ends, or (iii) a variable branching rate. Several examples are gi ven. We point out that geometrical and physical properties (skeleton d imension, percolation exponents, self-avoiding walk) of fractal trees depend strongly on their type. The most striking result is that the cr itical 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).