When activated, a bunch of asteroids appear within scanner range, moving randomly. If any of them move out of scanner range, they re-appear on the opposite edge on the same vector (same direction and velocity). As the asteroids are shot into boulders, the boulders exhibit the same behaviour and ditto for the splinters.
Eventually, all the splinters are scooped or shot: then suddenly more asteroids appear but more than the first time and moving slightly faster. And when they are all wiped out, even more, faster ones appear. And so on, thereby increasing the difficulty level.
There you have it: Asteroids the video game ... as a 3D 1st person shooter!

For version 1.1 ... a little Thargoid appears at the edge of scanner range and wanders along, shooting randomly in the general direction of the player, until it witchspaces out at the far end.