Universe

The Mandelbrot Set is a Universe in its own right.

In Wikipedia, The Universe is defined as "everything that physically exists, the entirety of space and time, all forms of matter, energy and momentum and the physical laws that govern them".

Here's another definition: The universe is a self-contained (or closed), potentially infinite, dynamical system with very specific laws and behaviours.
I think this definition can easily be applied to the Mandelbrot Set construct.

The Mandelbrot Set is a self-contained, potentially infinite, surprisingly dynamic system with very specific rules and behaviours.
This seemingly static “mathematical field” is capable of generating a variety of dynamics that, on closer examination, seem to closely resemble the dynamics and forces that we see in our very own universe.