Stealing a frame from 3blue1brown's video which points out that each region of the set has its own properties. In the case highlighted it cycles around 3 values. We already noticed that each region is built around a fixed point solution to an order of depth of the equation. The central cardioid is the fixed point for the 1st iteration. Values contract to a limit. The circular region is built around fixed points to the second iteration, and the system cycles between 2 values. Shown is a fixed point to the 3rd iteration and this has 3 values.
Hypothesis: the number of values the set cycles between is equal to the number of iterations of the equation the local fixed point solves.
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