This section is organized to be a possible tutorial of the CPS primarily up to the Eikosany. A reading of the first four of Wilson's paper here should be undertaken before proceeding with the papers below.
Where as traditional western music has a basic example of the "the cycle of 5ths", Each of Wilson's different lattices views presents patterns that can be thought of as fundamental to the structure. Each has it advantages and disadvantages. it is of upmost importance that one becomes familiar with these in sound as what is difficult in terms of visuals and intellectual comprehension is actually easier to grasp with the ear.
This chart can be thought of as an after the fact basis of the patterns illustrated within the various lattices below.
Here is possibly the most common view of the Eikosany. Many patterns are easily seen and mapped to it making it an ideal place to start. As Wilson points out on pages 21-22 of https://www.anaphoria.com/CPStoC-pt1.pdf each connecting line will involve the factor one places in the middle of the pentad. It is worth while to experiment with placing each factor in the center position to experience how it influences the overall sound in working with this structure. Thus starting with these 6 different versions of this lattice for the Eikosany is recommended. The choice of how the other factors are placed are of lesser importance in my own experience as the different patterns cover many of these variations.
The advantage of this lattice is that it is not biased toward any factor, and serves well to view the eikosany divided into patterns that repeat at 3 and 6 steps. The placing of the order of the each factor is of more importance here where those adjoining will occur more prevalent then those farther in the chain.