A New Type of Hierarchical Formations and the Structure

Abstract

In Chapter 2 for a particular example the system (2.24) and inequality (2.25) was associated with a hierarchical formation, which had two distinctive forms. In the first form, the elements are integer relations suggesting that the ultimate building blocks are integers from which “everything” develops as one whole. In the second form, the elements are two-dimensional geometric patterns, i.e., the integer patterns. The example helps us to understand that the hierarchical formation constitutes one possible hierarchical formation among many others admitted by a larger structure. This naturally motivates us to consider and define this structure.