Entries with the same color belong to the same faction.
The colors are basically red, blue, yellow and green, indicating the four quadrants.
The shade of this color is determined by the consul weight. The smaller one corresponds to the light shade.
The light and dark part of each matrix is the intersection of truth tables and Zhegalkin indices of great dominions. (See here.)
E.g. the dark part of this matrix is the intersection of T 14 and Z 8. In the caption this is expressed by the pair (14, 8).
The other shade in the same matrix has the reversed pair. (Gentle factions have pairs with equal entries.)
Different small clusters in the same big cluster have the same patron dominion.
A third relationship between factions is flipping the highest bit. (Flipping of the lowest bit is implied from the two others.)
Big clusters are defined with all three relationships. There are 8 of them.
Their entries in the 16×16 matrix form 2×2 squares, essentially making them entries of an 8×8 matrix.
(This means, that the lowest and highest bit are irrelevant to big clusters.)