Ij. Tsang et al., Cluster diversity and entropy on the percolation model: The lattice animalidentification algorithm, PHYS REV E, 62(5), 2000, pp. 6004-6014
We present an algorithm to identify and count different lattice animals (LA
's) in the site-percolation model. This algorithm allows a definition of cl
usters based on the distinction of cluster shapes, in contrast with the wel
l-known Hoshen-Kopelman algorithm, in which the clusters are differentiated
by their sizes. It consists in coding each unit. cell of a cluster accordi
ng to the nearest neighbors (NN) and ordering the codes in a proper sequenc
e. In this manner, a LA is represented by a specific code sequence. In addi
tion, with some modification the algorithm is capable of differentiating be
tween fixed and free LA's. The enhanced Hoshen-Kopelman algorithm [J. Hoshe
n, M. W. Berry, and K. S. Minser, Phys. Rev. E 56, 1455 (1997)] is used to
compose the set of NN code sequences of each cluster. Using Monte Carlo sim
ulations on planar square lattices up to 2000x2000, we apply this algorithm
to the percolation model. We calculate the cluster diversity and cluster e
ntropy of the system, which leads to the determination of probabilities ass
ociated with the maximum of these functions. We show that these critical pr
obabilities are associated with the percolation transition and with the com
plexity of the system.