Nesting Fractal Dimensions With Additive Cellular Automata in the 7-DTorus

Within the Behavioral Log Manifest, or BLM, there are a total
of eight "additive" or "nested" cellular automata out of the
256 "elementary" or aforementioned possible combinations of
allophonemic pink noise frequencies that are used to triangulate
the phase lock on the pilot wave, or the type 1 biophysical-
semeiotic sings. The number of rules for these nested types of
cellular automata with k colors and range r are exactly k^(2r+1).

Each "nest" is obtained by taking the cells in its neighborhood
and adding them in the fashion of modulo k, to yield the
"nested" pattern. These "patterns" are subsequently identified
with one of their seven-fold symmetric partner, or "thunder",
as it relates to one of the non-zero seven nested types (out of
the 256 other, non-nested types). These are systems of repetitive
behavior with no long range communication. A generalization for
the depth of this fractal dimension is probability distribution,
which becomes defined by the mean, variance, and other moments.

Now imagine each k value as the border defining the shape of the
fractal in space-time, nested to the degree of complexity required
by some resolution of its pilot wave or BLM signature, and you end
up with the toroidal continuum of seven, non-overlapping bound-
aries of k values, or colors, which have become nested to some
degree of complexity, or phase resolution, which has become set
by the allophonemic pink noise sequences.

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