We study a singularly perturbed scalar reaction-diffusion
equation on a bounded interval with a spatially inhomogeneous
bistable nonlinearity. For certain nonlinearities, which are
piecewise constant in space on $k$ subintervals, it is possible
to characterize all stationary solutions for small $\varepsilon$
by means of sequences of $k$ symbols,
indicating the behavior of the solution in each subinterval.
Determining also Morse indices and zero numbers of the equilibria
in terms of the symbol sequences, we are able to give a criterion
for heteroclinic connections and a description of the associated
global attractor for all $k$.