  We study the folding of the regular two-dimensional triangular lattice
embedded in the regular three-dimensional Face Centered Cubic lattice, in the
presence of quenched random spontaneous curvature. We consider two types of
quenched randomness: (1) a ``physical'' randomness arising from a prior random
folding of the lattice, creating a prefered spontaneous curvature on the bonds;
(2) a simple randomness where the spontaneous curvature is chosen at random
independently on each bond. We study the folding transitions of the two models
within the hexagon approximation of the Cluster Variation Method. Depending on
the type of randomness, the system shows different behaviors. We finally
discuss a Hopfield-like model as an extension of the physical randomness
problem to account for the case where several different configurations are
stored in the prior pre-folding process.
