Wreath Formulation of Sweep Representations

Abstract

Nearly all the representations developed in this book are sweep representations - the movement of some object (e.g., a curve) along a path. The reason for this is that, according to our theory, generativity is maximized by making the representation a wreath c-polycyclic group; i.e., a group that can be decomposed as a wreath product of c-cyclic groups. Each c-cyclic group represents the time parameter - i.e., the parameter along which generativity takes place. In a wreath c-polycylic group, each level represents the time parameter, and generativity is maximized by maximizing transfer, i.e., control-nesting the time parameter. One can say therefore that the entire object is swept out; i.e., each level sweeps out the previous level - all the way down.