  We present simulations of 2-d site animals on square and triangular lattices
in non-trivial geomeLattice animals are one of the few critical models in
statistical mechanics violating conformal invariance. We present here
simulations of 2-d site animals on square and triangular lattices in
non-trivial geometries. The simulations are done with the newly developed PERM
algorithm which gives very precise estimates of the partition sum, yielding
precise values for the entropic exponent $\theta$ ($Z_N \sim \mu^N
N^{-\theta}$). In particular, we studied animals grafted to the tips of wedges
with a wide range of angles $\alpha$, to the tips of cones (wedges with the
sides glued together), and to branching points of Riemann surfaces. The latter
can either have $k$ sheets and no boundary, generalizing in this way cones to
angles $\alpha > 360$ degrees, or can have boundaries, generalizing wedges. We
find conformal invariance behavior, $\theta \sim 1/\alpha$, only for small
angles ($\alpha \ll 2\pi$), while $\theta \approx const -\alpha/2\pi$ for
$\alpha \gg 2\pi$. These scalings hold both for wedges and cones. A heuristic
(non-conformal) argument for the behavior at large $\alpha$ is given, and
comparison is made with critical percolation.
