We employ the fully three-dimensional simulation to study the role
of magnetic fields and ion-neutral friction in regulating
gravitationally driven fragmentation of molecular clouds.
An initial random flow is input into a self-gravitating gas layer
that is threaded by a uniform magnetic field (perpendicular to the layer).
The cores in an initially subcritical cloud develop gradually over
an ambipolar diffusion time while the cores in an initially supercritical
cloud develop in a dynamical time. We found that a snapshot of the relation
between density ($¥rho$) and the strength of the magnetic field ($B$) at
different spatial points of the cloud coincides with the evolutionary
track of an individual core. When the density becomes large, both the
relations tend to $B ¥propto ¥rho^{0.5}$. We also have demonstrated that
the formation of collapsing cores in subcritical clouds is accelerated by
the supersonic nonlinear flows. Although the time-scale of the core
formation in subcritical clouds is a few $¥times 10^7$ years when starting
with small subsonic perturbations, it is shortened to approximately
several $¥times 10^6$ years by the supersonic flows.
The result is consistent with previous two-dimensional simulations.