  Directed spiral percolation (DSP), percolation under both directional and
rotational constraints, is studied on the triangular lattice in two dimensions
(2D). The results are compared with that of the 2D square lattice. Clusters
generated in this model are generally rarefied and have chiral dangling ends on
both the square and triangular lattices. It is found that the clusters are more
compact and less anisotropic on the triangular lattice than on the square
lattice. The elongation of the clusters is in a different direction than the
imposed directional constraint on both the lattices. The values of some of the
critical exponents and fractal dimension are found considerably different on
the two lattices. The DSP model then exhibits a breakdown of universality in 2D
between the square and triangular lattices. The values of the critical
exponents obtained for the triangular lattice are not only different from that
of the square lattice but also different form other percolation models.
