  This study analyzes the sizes, shapes and correlations of $\lya$ clouds
produced by a hydrodynamic simulation of a spatially flat CDM universe with a
non-zero cosmological constant ($\Omega_0=0.4$, $\Lambda_0=0.6$, $\sigma_8
=0.79$), over the redshift range $2\le z \le 4$. The $\lya$ clouds range in
size from several kiloparsecs to about a hundred kiloparsecs in proper units,
and they range in shape from roundish, high column density regions with
$\nhi\ge 10^{15} cm^{-2}$ to low column density sheet-like structures with
$\nhi \le 10^{13} cm^{-2}$ at z=3. The most common shape found in the
simulation resembles that of a flattened cigar. The physical size of a typical
cloud grows with time roughly as $(1+z)^{-3/2}$ while its shape hardly evolves
(except for the most dense regions $\rho_{cut}>30$). Our result indicates that
any simple model with a population of spheres (or other shapes) of a uniform
size is oversimplified; if such a model agrees with observational evidence, it
is probably only by coincidence. We also illustrate why the use of double
quasar sightlines to set lower limits on cloud sizes is useful only when the
perpendicular sightline separation is small ($\Delta r \le 50h^{-1}$ kpc).
Finally, we conjecture that high column density $\lya$ clouds ($\nhi\ge 10^{15}
cm^{-2}$) may be the progenitors of the lower redshift faint blue galaxies.
This seems plausible because their correlation length, number density
(extrapolated to lower redshift) and their masses are in fair agreement with
those observed.
