SIDEBRANCHING IN NOISELESS DIFFUSION-LIMITED AGGREGATION

Abstract

The equivalence between diffusion-limited aggregation (DLA) and growth in a Laplacian field is exploited to construct an algorithm for the simulation of DLA at large finite noise reduction. This algorithm allows performing of the limit towards infinite noise reduction, yielding a feasible prescription for the simulation of the noiseless, i.e., deterministic limit. Contrary to previous expectations as well as explicit predictions from an analytic theory, clusters grown without noise develop sidebranches. An explanation of this result in terms of the outer radius used in DLA simulations is suggested. Various implications, including the question whether or when noise reduction may accelerate the approach to asymptotic behavior, are discussed.