<< I'm more interested in a much more basic version of this question. I have heard that the concept of fractals and the math behind them have influenced weather forecasting, mapmaking (apparently shorelines tend to conform to fractal equations?), and other fields, but how has fractal math affected astronomy and/or astrophysics? >>
The scientists originally applied the fractal concepts to terrestrial sciences, but neglecting to mention the possibility of applicability to other fields, the effers were too stupid to ask. I'm guessing here, but reasonably sure it's true. How many times do I have to prove their competence level?
