An epidemic analysis of individually-grown clusters was performed to determine their critical thresholds pc. According to the method, the boundaries of the lattice are never seen so the irregular nature of the quasilattice boundary is irrelevant. Since new issues concerning the need to average over different lattice environments are becoming evident, the usual epidemic analysis was extended to account for corrections-to-scaling behavior. To confirm the method, simulations were carried out on the square and triangular lattices at their pc. Site percolation on the Penrose rhomb lattice is discussed.
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