Conformal Theory of the Dimensions of Diffusion Limited Aggregates

Details Conformal Theory of the Dimensions of Diffusion Limited Aggregates Conformal Theory of the Dimensions of Diffusion Limited Aggregates

1998-12-20

arxiv.org/abs/chao-dyn/9812026v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 3 figures, submitted to Phys. Rev. Lett

Scientific paper

10.1209/epl/i1999-00518-y

We employ the recently introduced conformal iterative construction of Diffusion Limited Aggregates (DLA) to study the multifractal properties of the harmonic measure. The support of the harmonic measure is obtained from a dynamical process which is complementary to the iterative cluster growth. We use this method to establish the existence of a series of random scaling functions that yield, via the thermodynamic formalism of multifractals, the generalized dimensions D(q) of DLA for q >= 1. The scaling function is determined just by the last stages of the iterative growth process which are relevant to the complementary dynamics. Using the scaling relation D(3) = D(0)/2 we estimate the fractal dimension of DLA to be D(0) = 1.69 +- 0.03.

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