# Hexagram Navigator

## Pattern of Opposition Index

These groups describe the patterns that arise by relating the different types of opposition. Each equation defines a particular pattern which applies to a given group of hexagrams. These groups are directly related to contrast clusters, each pattern of opposition group is composed of a number of clusters.

~P = o(P) = e(P) - all forms of opposition agree with each other

P = o(P) = e(P) - the structural oppositions are invariant

~P = o(P) - Boolean opposition and structural overturning agree

~P = e(P) - Boolean opposition and structural exchange agree

P = o(P) - structural overturning is invariant

P = e(P) - structural exchange is invariant

o(P) = e(P) - structural overturning and exchange agree

Half of the hexagrams do not fit into any of the above patterns, there are no equalities between any of the opposition operators. They are all in the following set:

~P ≠ o(P) ≠ e(P) and P o(P) and P e(P) - all the forms of opposition are unique