You will find passages in Synergetics wherein Fuller is indeed exploring the growth rates associated with expanding outward and he anticipates fractal growth by packing more and more “between the balls” of a conventional 3rd power growth rate (in volume).
That would correspond to upping the dimension number from “within” the next lower dimension. Similar fractal games approach 2D from a 1D basis or 3D from 2D. Hausdorff Dimension.
https://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension
https://www.hindawi.com/journals/physri/2011/874302/
I’ll be going to look for those passages (it may only be one) and follow up.
However, I think his eventual meaning for 4D, as Synergetics progressed, is quite precise and involves dismissing 0, 1, 2, 3D as unnecessary i.e. his points, lines, planes (all internally defined) occupy volume and volume is primitively a container and the primitive container is 4 directional (4D).
Wait, we said “dimensional” not “directional”. True, but then “dimension” is a fishy word to begin with, and it relates to “directional”.
