  We reproduce the symmetric and asymmetric ``rippled'' $P_{\beta'}$ states of
lipid membranes by Monte Carlo simulations of a coarse-grained molecular model
for lipid-solvent mixtures. The structure and properties compare favorably with
experiments. The asymmetric ripple state is characterized by a periodic array
of fully interdigitated ``defect'' lines. The symmetric ripple state maintains
a bilayer structure, but is otherwise structurally similar. The formation of
both ripple states is driven by the propensity of lipid molecules with large
head groups to exhibit splay.
