Hierarchical self-similarity does seem to be ubiquitous, and a lot of people have taken this idea and run with it. I think Hofstadter's GEB is one of the crucia

Hierarchical self-similarity does seem to be ubiquitous, and a lot of people have taken this idea and run with it. I think Hofstadter's GEB is one of the crucial modern texts that inspired a lot of people in that direction. Translating these concepts into rigorous theories is difficult; attempts like Wolfram's "A New Kind of Science" haven't succeeded in creating a new discipline. I think the deepest explanations for the layering of complex structures at multiple scales we see in the universe are being developed at the intersection of the theory of computation and quantum physics. There is a very tight coupling of entropy and information at the quantum scale, as demonstrated by physicists like the amazing W.H. Zurek. The development of quantum computers and work on the P/NP equivalency problem is where I hope to see the long-awaited breakthroughs that may enable us to understand just how math, mind, and physics are intertwined.