We discuss results from numerical simulations of star formation
under various environmental conditions ranging from the turbulent
interstellar medium to low-mass halos in the early universe. The
thermodynamic behavior of the star-forming gas plays a crucial role
in fragmentation and determines the stellar mass function as well as
the dynamic properties of the nascent stellar cluster. The
thermodynamic state of the gas is a result of the balance between
heating and cooling processes, which in turn are determined by
atomic and molecular physics and by chemical abundances. Features in
the effective equation of state of the gas, such as a transition
from a cooling to a heating regime, define a characteristic mass
scale for fragmentation and so set the peak of the initial mass
function of stars (IMF). As it is based on fundamental physical
quantities and constants, this is an attractive approach to explain
the apparent universality of the IMF in the solar neighborhood as
well as the transition from purely primordial high-mass star
formation to the low-mass mode observed today.