  We present a series of simulations of the fragmentation of a molecular cloud,
leading to the formation of a cluster of protostellar cores. The purpose of
these simulations is to address a specific numerical problem called artificial
fragmentation, that plagues SPH simulations of cloud fragmentation. We argue
that this is a serious problem that needs to be addressed, and that the only
reasonable and practical way to address it is to use a relatively new technique
called particle splitting. Our largest simulation has an effective resolution
of 256^3 particles (much higher than most previous SPH simulations of cloud
fragmentation) and results in the formation of a dense cluster containing ~3000
protostellar cores. It is the first simulation of this kind to properly resolve
the Jeans mass throughout the entire system, at all times, thus preventing
artificial fragmentation.
