  We study, on a square lattice, an extension to fully coordinated percolation
which we call iterated fully coordinated percolation. In fully coordinated
percolation, sites become occupied if all four of its nearest neighbors are
also occupied. Repeating this site selection process again yields the iterated
fully coordinated percolation model. Our results show a substantial enhancement
in the size of highly connected regions after each iteration (from ordinary to
fully coordinated and then to iterated fully coordinated percolation). However,
using Monte Carlo methods to determine the static critical exponents and normal
mode analyses to determine the dynamic critical exponents, our results indicate
that the ordinary, fully coordinated, and iterated fully coordinated
percolation models belong to the same universality class. This is in contrast
to our previous results [*] wherein a different universality class dynamically
(but not statically) for fully coordinated percolation was indicated, though
the differences in the dynamic exponents were small. A possible cause might be
the different methods of generating clusters, i.e., in this work clusters were
generated statically in square lattices while in our previous work clusters
were grown dynamically, for studying the dynamic critical exponents.
  * E. Cuansing, J. H. Kim and H. Nakanishi, Phys. Rev. E, 60, 3670 (1999).
