The spectral dimension $d_s=\frac{2d_f}{d_w}$ is calcualted for the diffusion-limited aggregation model of colloids and dendritic growth; here $d_f$ is the fractal dimension of the aggregate, and $d_w$ the fractal dimension of a random walk on the cluster substrate. $d_s=1.2-1.4\mathrm{}$ is found for $d=2\mathrm{} \mathrm{and} 3$, to within the accuracy of the present Monte Carlo calculations. Thus Witten-Sander aggregates may possess the same remarkable "superuniversality" discovered for percolation clusters and argued to possibly hold for all homogeneous fractals.

• Received 4 August 1983

DOI:https://doi.org/10.1103/PhysRevLett.51.1457