I'm interested in fractals, self-similarity, and chaos. Many physicists disregard these phenomena as candidates to explain the fundamental properties of the universe. However, when I read about concepts such as renormalization, and non-linear PDEs I feel as though some of the concepts I mentioned are already incorporated in our physical theories and could even be extended.
My question is this. Can I study fractals, renormalization, chaos, self-similarity, as they relate to physics, and not be labeled a "crank"?
It should be kept in mind I live in a near scientific vacuum. Neither of my parents are scientists and I'm in high school so I can't read the newest/relevant literature. I do have a mathematical background for QM, Fluid Mechanics, Classical Mechanics. I also know the basics of perturbative techniques for QFT. I also have knowledge of fractal geometry and dynamical systems.