Are Random Fractal Clusters Isotropic?

We have studied the shape of large clusters in the lattice-animal, percolation, and growing-percolation models. By calculating the radius of gyration tensor we find that in these models the clusters have an anisotropic shape. The results suggest that the critical droplets in related isotropic equilibrium models, such as the Ising model, may also be anisotropic. We have also determined the leading nonanalytic correction-to-scaling exponent by analyzing the anisotropy data and find that for percolation in two dimensions $\theta \simeq 0.47$.