Wave Functions

There are a number of different ways of defining wave movement within hexagrams. The most interesting, from the point of view of their connection with internal energy boundaries and Chorand spheres, is the circular (or cyclic) function. We shall begin with this function.

The Cyclic Function

This function is defined in terms of an operation that would be known in computing circles as a circular buffer rotation, or bit rotation, sometimes called rotate through carry. The animation of the left shows the effect on the lines of the hexagram; they continually rotate up through the structure and, as a line reaches the top and leaves, it rejoins the structure at the bottom. For example, consider the hexagram - after the lines have been rotated up through one step, the result will be , the yang line at the top appears at the bottom and everything else moves up one place.

Note that this always creates repeating sequences of hexagrams. If we start with and apply the circular function 5 times, the yang line will have moved up to the top place . If the function is applied once more, then the first hexagram arises again.  The animation below shows this:

Clearly, this will work regardless of the pattern of yin and yang within the hexagram. For example, if we start with Sunken Light then the pattern shown in the animation below emerges.  Notice how, for much of the sequence, it can easily be seen as a Fire trigram rising up through the structure, but once the top yang line wraps around to the beginning again, the visual pattern breaks down until things return to the starting point.

The exact nature of the wave and the length of the sequence depends on which hexagram is fed into the function to get things started. Feeding any gua from a complete sequence into the circular rotation function gives the same sequence.

Contrasts with the Boolean Lattice

For the Boolean lattice, the defining relationship is the partial order ≤ which defines up and down.  This is a dimensional/energetic relationship, and there is no temporal aspect. In the case of a sequence, where one hexagram follows another, it makes more sense to talk in terms of "next" and "previous"; there is a definate temporal aspect.  

Further, in a wave sequence, the energy level of the hexagrams does not change - there is always the same amount of yang energy in the wave.  This contrasts with the lattice order, where the amount of yang energy goes up or down depending on which direction one moves through the lattice.