From Osher Doctorow (not Marleen Doctorow)

I have been arguing on http://www.superstringtheory.com/forum, in the Strings/M Duality subforum of their Forum section, that fractals relate directly to expansion-contraction of the universe. In the cosmology branch of physics and mathematical physics (the latter is technically a branch of mathematics), where I spend much of my time, there is considerable interest in the expansion, contraction, and acceleration of the universe. The most unusual thing about expansion-contraction is that it differs from ordinary curvilinear or linear motion in involving GLOBAL and CONTROL properties - a whole bunch of coordinated parts of an object like a balloon expand or contract simultaneously, and theoretically different parts of an object can be controlled to expand at different rates. Up to this point in my posting, it doesn't look as though fractals and expansion-contraction have anything unusual about them, but now notice that the SURFACE of a balloon is critically involved in its expansion- contraction. The SURFACE, not just the volume, expands in coordination, and the surface reflects different rates of expansion. 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.). It might be agreed by readers that Fractals are related to expansion- contraction as surfaces, but what does this have to do with the Univese other than the fact that the Universe is supposed to be expanding? 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. Most things move curvilinearly (in a curve) or linearly (in a straight line). They don't blow up or contract like balloons. Here's a list of things in the Universe that do expand-contract as their characteristic motions. A. The whole universe itself as for example in the usual spherical model. B. Radiation (light, heat, etc.) from a source (a point or string) C. Biological life (growth, muscular movements, etc.) D. Human consciousness, memory, perception E. Galaxies (evolving with expansion or contraction from spiral to elliptic, etc.) F. Organic materials such as plastics which have viscoelasticity. David J. Wright (Oklahoma State) "Dynamical systems and fractals lecture notes," 8-19-96, www.math.oksate.edu/mathdept/dynamics/lecnotes/lecnotes.html, explains very clearly how fractals are generated by CONTRACTIONS of iterated function systems (IFS), either linear or hyperbolic. 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. Osher Doctorow Ph.D. One or More of California State Universities and Community Colleges