If the lenticular lens is made of columns (as those fake 3D postcards are) then only horizontal shift is 3D-able. To display verticality, the lenticular lenses

If the lenticular lens is made of columns (as those fake 3D postcards are) then only horizontal shift is 3D-able. To display verticality, the lenticular lenses could be hemispheres. However, to encode vertical 3D-ness you would need 45 images for each 2 degrees off the horizontal so as your head bobs up and down, it can pick up the off axis images. So that's 45 images x 45 axes = 2025 images per frame.