This is an attempt to redefine m-branch subsets in off-lattice two-dimensional diffusion-limited aggregation simulations, where m is the number of particles of a branch which lacks a hierarchy of order. In our simulations, the total number of aggregated particles N behaves as N = (2R)(D), where R is the radius of gyration of the cluster and D is the fractal dimension. The number of in-branch subsets M-m(R) depends on R as M-m(R) = A(m)R(D) and the subsets are D-dimensional self-similar fractals. These results show that the probability distribution of the subsets is stable, and has a peak at m = 2, and that the subset at m = 2 is the most observable of all the subsets independent of time. [References: 19]
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