Statistical Physics

Tracing a diffusion-limited-aggregate: self-affine versus self-similar scaling

The geometry of diffusion-limited aggregation clusters is mapped into single-valued functions by tracing the surface of the aggregate and recording the X (or Y) coordinate of the position of a walker moving along perimeter of the cluster as a function of the arc length. Our numerical results and scaling arguments show that the related plots can be considered as self-affine functions whose scaling behavior is determined by the exponent H=1/D, where D is fractal dimension of the aggregates.


More publications
A.-L. Barabási, P. Szepfalusy, T. Vicsek

Physica A 178, 17–28 (1991)

S.V. Buldyrev, A.-L. Barabási, F. Caserta, S. Havlin, H.E. Stanley, T. Vicsek

Physical Review A 45, R8313–R8316 (1992)