loop symmetry1
symmetric element
antisymmetric element
An infinite variety of patterns can be generated with the simple element of a line with a loop on either end. There is surely a mathematical theory that maps directly to all of the distinct topological patterns that can be generated. Here I only note that the patterns with symmetric pairing of loops creates a simple interpretation of foreground and background spaces. Antisymmetric elements or pairing creates illusion of a locally sensible but globally impossible surface.
antisymmetric pairing symmetric pairing