Can We Do Science on the Mandelbrot Set?

If you notice, one of the most recognizeable features of the Mandelbrot set is a cardioid shape when completely zoomed out. Imagine looking for all the other patterns that are present in the Mandelbrot set which might be computational shortcuts describing features of the real world.

What if intractible mathematical puzzles could be solved just by measuring some aspect of this mathematical object?

Anyway, I'm going to try :)