Fractal Scale Invariance

Fractional dimensional curves are a good place to start with the analysis of physical phenomena in the universe. From the distribution of photons in the CMB to biological systems and the complex adaptive systems that have evolved in the world we observe today, scale invariant systems are the nature of reality. Perturbations to infinite order, to first order to begin with, can help define the symmetry of fractal expansions and distributions of partition functions, quantum states, thermodynamics systems, and biological models. In essence, the fractal is the generator of the observation. In the logical paradigm, it would make sense that what is observed in the universe is just a reflection of the measurement problem, meaning that the fractal generator is observed and also a fundamental particle like state. Of course, General Physics' scientists are working on new Weyl topological interpretations of space as opposed to the Euclidean and Cartesian world. Pythagoras is a local and nearest neighbor paradigm, that, although generates interesting self-similar artifacts, neglects the hyperspace non-local spooky action at a distance of quantum. This harkens in the era of fractal space as the progenitor or all phenomena, basically described by a Riemann zeta function which is fractal in the gamma function and beta function expansions. The theory was discussed in grad school and in mathematics journals. In any case, look for more fractal discussion in the future.