  The morphology of the total gas and the neutral hydrogen (H I) distributions
during the cosmological epoch of reionization can be quantified with Minkowski
Functionals (MFs) of isodensity surfaces. We compute the MFs from the output of
a high-resolution numerical simulation which includes explicit treatment of
transfer of UV ionizing radiation. "Galaxies" identified in the simulation
using semi-analytic models of galaxy formation are assumed to be the sole
sources of UV photons. The MFs of the total gas distribution are well described
by the analytic expressions derived for lognormal random fields. The
statistical properties of the diffuse H I depend on the gas distribution and on
the way ionized regions propagate in the inter-galactic medium (IGM). The
deviations of the MFs of the H I distribution from those of a lognormal random
field are, therefore, caused by reionization. We use the MFs to discriminate
between the various stages of reionization in the simulation. We suggest a
simple model of reionization which reproduces the MFs derived from this
simulation. Using random realizations of lognormal density fields, we also
assess the ability of MFs to distinguish between different reionization
scenarios. Our results are relevant to the analysis of future cosmological
twenty-one centimeter maps.
