  In this paper, we investigate the large-time behavior of bounded solutions of
the Cauchy problem for a reaction-diffusion equation in $\mathbb{R}^N$ with
bistable reaction term. We consider initial conditions that are chiefly
indicator functions of bounded Borel sets. We examine how geometric
transformations of the supports of these initial conditions affect the
propagation or extinction of the solutions at large time. We also consider two
fragmentation indices defined in the set of bounded Borel sets and we establish
some propagation or extinction results when the initial supports are weakly or
highly fragmented. Lastly, we show that the large-time dynamics of the
solutions is not monotone with respect to the considered fragmentation indices,
even for equimeasurable sets.
