Osher Doctorow (not Marleen Doctorow) writes:

I have been arguing [...] that fractals relate directly to expansion-contraction of the universe.

"Directly" perhaps remains to be seen. The idea of surfaces is interesting, though. I've read that some fractal "purists" only ever color the Mandlebrot in two colors: inside & outside.

The most unusual thing about expansion-contraction is that it differs from ordinary curvilinear or linear motion in involving GLOBAL and CONTROL properties...

How does this really differ from ordinary movement, which also would seem to involve GLOBAL and CONTROL properties? For example, doesn't the earth's orbit involve properties "global" to the system (e.g. the earth's mass) as well as "control" properties (e.g. gravity)? It would seem that motion through space of an object where the object does not change form is distinct from motion involving a form change. In my experience, the term "orthogonal" is sometimes used to refer to properties that are not related. I would think that shape-changing movement is orthogonal with respect to non-shape-changing movement. Certainly some objects may do both. Throughout my life, my shape has changed (mostly gotten larger!), but I have also constantly moved through space (and time).

Fractals are BOUNDARY phenomena, and therefore are vitally related to surfaces which are also boundaries of their insides and outsides in 3 dimensions, or to projections of surfaces in 2 dimensions (boundaries of continents, leaves, trees, etc.).

There are many BOUNDARY phenomena, however. Is not the most salient aspect their fractal dimensionality? Do the expansion/contraction phenomena under study here demonstrate this? If not, I would question the connection.

It might be agreed by readers that Fractals are related to expansion- contraction as surfaces,...

The relation seems tenuous thus far. The fractal dimension aspect seems missing or not covered. Further, a given fractal seems static; neither expanding nor contracting.

Well, it turns out that there aren't that many types of objects in the Universe which are expanding or contracting as their characteristic motions.

[grin] Yet your own list names some rather significant ones! After life, thought, energy and the entire universe, what's left? (Incidentally, I would add metals and water to that list.)

There is some prospect that not only can we generate fractals in the above manner, but that ALL expansion-contraction objects obey similar algebraic and calculus/analysis/differential equation formulas which sharply distinguishes them from ordinary objects which only have curvilinear or linear motion. I'll try to keep readers informed of major developments as they occur.

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