Actually space is full of fields, which as far as we know are continious. They exist at every point in space. But that in itself is probably an approximation.
So it was easier for me to talk of axions like they were particles. And to some extent they behave like the ocean- I liked the analogy of whales transmitting signals around the oceans of the earth. Clearly, signals is what counts in the axionic media. It's an information storing and communicating medium.
But we also know from quantum physics that particles only come into existence when quantum fields interact nonlinearly- and as a byproduct produce mass. Thus the fields in a solid substance are continiously interacting with each other, and the approximation that they are continiously existing matter partcles is a very accurate one.
But for example let's consider electromagnetic waves, which are a form of quantum fields. We now know that light is either fields or particles, not both at the same time. In fact, light is almost all the time fields and only becomes a particle, or rather acts like what we think particles act like, (science is really all analogy), for instants of time when undergoing nonlinear interaction with other fields.
So, how does this apply to axions. Well, axions, being purely quantum particles (a misnomer) are actually purely fields all of the time. The fields still have gravitational attraction, just like light is gravitationally attracted to the sun- astronomers measure the bending of kight rays as they pass by the sun. So the axion fluid is more like a universal field than a form of ether.
To me that makes the supernatural all the more mysterious. Come to think of it, quantum effects make the physical world pretty mysterious as well.