The rate of growth
and period of oscillation of the width of the dendritic crystal arm appear to be roughly the same as the
corresponding numbers for
the radius of the dendrite, but precisely out of phase.

Recall that the
terms of 2-fold operads of Young diagrams, minimal relative to a given starting sequence, do take turns
increasing in size vertically
and horizontally. However, the length of a “side-branch” grows only logarithmically.

But, the number of
blocks in the entire structure grows linearly. Thus the number of blocks to the right of the first column
grows at the same average
rate as the height of the first column. These two growth rates oscillate out of phase, just as is seen in
the crystal.