A Method of Stereoptically Simulating Manifolds of Three-Dimensional Objects Using Only a Single Display Pattern: A Shape-Depth-Texture Invariance

A means of conceptualizing and generating visual displays that are “self-stereoptic manifolds” is described. First, single patterns that can replace pairs of stereograms to produce illusions of depth are defined and an example is shown. Patterns such as these produce illusory three-dimensional objects hanging in space before or behind the display surface. It is further demonstrated geometrically that such a display actually has three-dimensional information embedded in it peculiar to each of a family, or manifold, of objects that can be experienced one at a time. Each object of the family appears when the viewer looks in space where it “exists.” The others remain invisible unless their locations are fixated. If any member of a specific manifold of three-dimensional illusory objects is physically duplicated as a real object and textured in the same way that the illusory object appeared to be, then this new real object will, in turn, generate an illusion of each of the other objects of the manifold when the observer fixates in space where each “exists.” Also, if then the viewer looks where the original display previously was, the newly constructed object will disappear and the display will reappear. The geometry and the advantages and disadvantages in relation to a stereoptic pair are discussed.