The Mandelbrot set is much bigger than the entire physical universe. It is a universe of universes, infinite.
One could argue that those who explore it engaging in a type of astronomy, at least in an abstract sense.
In any event, I think that the type of curiosity that motivates one to explore the physical universe is probably related to the type of curiosity that motivates those who explore the Mandelbrot set.
"I have this philosophy of goodness. Mathematics should contain goodness. So in the case of the elliptic equation, one might call the equation good if it is parameterized by a modular form. I expect all elliptic equations to be good. It's a rather crude philosophy but one can always take it as a starting point. Then, of course, I had to develop various technical reasons for the conjecture. I might say the conjecture stemmed from that philosophy of goodness. Most mathematicians do mathematics from an aesthetic point of view and that philosophy of goodness comes from my aesthetic viewpoint."
This then newly discovered relationship twixt elliptic equations and modular forms, seemed secondary to Shimura if it was not "good". In the sense that mathematics seems wedded to the structure of the universe, I for example, take this as strong evidence for God in existence, especially given the recent discovery of another separate "language" encoded deep within the DNA molecule itself. This sense of "mapping" via mathematics and physics seems to me to undercut randomness being from what Creation was wrought.
mandelbrot...what does that have to do with almond bread?...darn I’m hungry!