The Big Bang (as a common source) determined the genesis and structure of laws, constants and limitations of both the macrocosm and the microcosm of the observable Universe. The unity of the structural and spatial levels of matter implies that there are connections between the laws, constants and limitations of the macrocosm and the microcosm. The scale factor masks these links. Using fractals to scale physical processes that take place at different structural and spatial levels of matter allows us to find connections between the macrocosm and the microcosm of matter:
Preprint FRACTAL GENESIS OF THE ANGLES OF THE NEUTRINO MIXING MATRIX....
Dear Dr Timkov
I appreciate your answer concerning the context that forms your perspective for Fractal. I'd like to add one or two comments. Because of my recent work with fractals I can no longer that Fractals are necessarily simply because Mandelbrot offered nothing but very generic sets of rules to bring them into existence. They originate from topology where there aren't rigorously things such as lengths, angles and therefore straight lines; A Euclidean dimension shouldn't be considered to be a fractal dimension that has the exact value of an integer value either.
I've been working working with Pascal's triangle and another set that's the generator for the Passoja-Lakahtakia set and have made considerable progress with the intention to incorporate fractal mathematics into quantum mechanics.
Pascal's triangle is relevant because it has a direct connection with probability. The PL set and its generator is something that I discovered in 1992. Both can be used to represent fractal sets by finding Mod[Prime] of them. I've found that by using Pascals Triangle Mod[2] accompanied by Mod[Primes]of the PL generator it's possible to produce the Mod[Prime{ ] fractal set. The sets are all different, fractal and I can solve some simple equations with them.
Since I found the Prime Fractal Sets I've stopped associating geometry with fractals. In had no need to use the recipes proposed by BBM. My method was matrix-based and rule-based made by using the simplest algorithms imaginable. I have recently explored algebraic equations and more {power series etc} in conjunction with matrix mathematics. Primes, have been a great motivator because they've been called the "atoms of the number system.
It's quite easy to look at a fractal image in a matrix and notice that it has a quite obvious relationship to geometry. However, at this point I've begun to accept the fact that it doesn't seem to fit in any categories very well.
Also, while searching the literature I've begun to notice that there's a tendency to use physical theories to rationalize mathematical considerations; for example the Uncertainty Principle and the meaning of limits, and since fractal surfaces are non-differentiable that differential calculus should be abandoned altogether. As far as I'm concerned these people don't really understand the basics and how and why they function.
Once again thanks for your response
Dann Passoja
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