Abstract
We consider the ``overlap pattern'' formed by the intersection of two diffusion-limited aggregation (DLA) clusters. The fractal dimension of the disconnected set of points belonging to the intersection is given by ${d}_{f}^{\ensuremath{\cap}}$=2${d}_{f}$-d, where ${d}_{f}$ is the fractal dimension of the original DLA, and d is the space dimension. We measure ${d}_{f}^{\ensuremath{\cap}}$ from simulations in d=2,3 based on two DLA clusters, and then calculate the corresponding value of ${d}_{f}$. Also, we use the more general equation ${d}_{f}^{\ensuremath{\cap}}$=${d}_{f}$+${d}_{f}^{\mathcal{'}}$-d to analyze overlap patterns obtained by slicing a d=3 DLA cluster with a ${d}_{f}^{\mathcal{'}}$=2 plane. We find good agreement with independent estimates of ${d}_{f}$ for DLA.
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