the interesting shape here looks fairly similar to an epitrochoid or epicycloid, if you're interested. It looks like it rolls around the circle from the centre of the smaller circle instead, though. Like this example:
It's a little bit complicated how it ended up as seen in the .gif.
The bullets you see are actually heat-seeking rockets. Their target-mode is to move towards the mouse arrow, which has not been recorded. I move it by hand around the spaceship, which additionally rotates the spaceship. The spaceship and the rockets have a maximum turning speed. I always keep the mouse arrow very close next to the emitter, moving it at the turning speed around the emitter always keeping it at the same relative position towards the ship.
The rockets also have acceleration speed. When they are accelerating they emit this blue line of pixels which can be seen right after they have been emitted, tha'ts how it ends up as an ellipse rather than a circle.
Yea it's complicated:)))))))))))))))))))))))))
But what's important: I can create really interesting effects for boss enemies in my game.
