'Quarks' and 'leptons' in three dimensional patterns

The following questions are addressed: How did the symmetries which lead to fractional invariants arise? Can one start with systems with much simpler symmetries, say space translation and rotation, and, by stressing such systems, give rise via phase transitions to objects with natural fractional invariants? Such systems are manifold in nature. They are called pattern forming systems. One has to go no further than one's own fingertips to see examples of two dimensional cross sections of the objects which are the centerpieces of this paper.