Earlier this year, I composed a model of Socionics based on a sine wave. I was just playing around, really, but recently I have seen signs that it might be useful.
A diagram of the LII:
The four elements that the wave passes closest to are the valued functions. The vital ring, across the bottom, has the most information (denoted by the darker grey). The id functions are fully competent (the information in the Thinking and Intuitive sections reaches almost to the top), but do not have any information input or output. The wave has a direction - either left or right - that results in input or output, depending on whether the wave is rising or falling (the wave must take in information to rise, thus increasing competency, and output informaiton to fall, decreasing competency). The superego functions have no information and no activity (unless the wave is distorted to accomodate them), and the superid functions are weak, but desire the same quantity of input/output as the ego functions.
In dynamic types, information rises toward the top, instead of falling to the bottom as it does with static types.
One of the first things I noticed was that a mirror has the same input/output as a dual. However, neither is competent in the other's superid, so the result is a perfect ego exchange - with little or no superid action.