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We study the folding of the regular two-dimensional triangular latticeembedded in the regular three-dimensional Face Centered Cubic lattice, in thepresence of quenched random spontaneous curvature. We consider two types ofquenched randomness: (1) a ``physical'' randomness arising from a prior randomfolding of the lattice, creating a prefered spontaneous curvature on the bonds;(2) a simple randomness where the spontaneous curvature is chosen at randomindependently on each bond. We study the folding transitions of the two modelswithin the hexagon approximation of the Cluster Variation Method. Depending onthe type of randomness, the system shows different behaviors. We finallydiscuss a Hopfield-like model as an extension of the physical randomnessproblem to account for the case where several different configurations arestored in the prior pre-folding process.Comment: 12 pages, Tex (harvmac.tex), 4 figures. J.Phys.A (in press

Folding of the triangular lattice in the face-centred cubic lattice with quenched random spontaneous curvature