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The structure of fjords in diffusion-limited aggregation ( D L A ) clusters can be described in terms of the loop size distribution n R ( x ) which is the normalised number of loops with a neck to depth ratio x within a circle of radius R centred at the origin of the cluster. We find from the numerical study of very large off-lattice aggregates that n R ( x ) converges quickly to a limiting distribution with a well defined smallest ratio x", larger than zero indicating the self-similarity ofdoi:10.1088/0305-4470/23/15/007 fatcat:27nicfcl2nc2ncync2aqph6sby