Second-Power Paired N-Grams

Tony has developed a set of equations {the Blake formulae} that define what I call "second power" N-Grams, a special subset of paired N-Grams. The enneagram is one of the figures that derive from these equations. (Terminology taken from a paper titled, N-Grams as a Tool for Researching the Organisation of Complex Systems.)

N = B - 1 = p * p and
p + q = B ; where
N is the number of points around an N-Gram, the effective or visible number of the structure
B is the numeric base, or wholeness number of the compund system or structure.
p and q represent the division of the whole into aspects.
I call p the informing number, and q the resolving number.

Progression of Complexity: The figures below are the second-power paired N-grams for values of p from 1 to 5. The black dots represent p. The top black dot along with all the colored lines together represent q. Colors are used to indicate the progression of pattern from one paired N-Gram to the next.

There is a regular pattern to the increasing complexity in these figures. Sets of patterns form. A new pattern first appears as a two-point pattern (examples above in the second and fifth figures). In the next pattern in sequence the two-point pattern is replaced with a six-point pattern. In following figures each sequence gets one additional six-point pattern. This progression is summarized below.