We study the branching structure of very large DLA clusters, of up to 100 million particles. The Horton-Strahler ordering of the branches in these clusters shows a relaxation towards a state with the stream numbers forming a geometric series. This behaviour is compared with those of several self-similar trees. It indicates that DLA clusters converge to topologically self-similar objects.
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Yekutieli et al. (1994) studied this question.
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