That knot of Saturn looks like art to me. Anyway hats off for being to play with geometry like that.

Is it just me, or does it look like black holes hovering over the planets? I guess that is to be expected, if a planet with black background is used. Pseudo-scientific question: Could black holes have anything to do with something being inverted?

A black hole is just an object with so much dense mass that its Schwarzschild radius[1^] extends outside of its body. Everything has a Schwarzschild radius.

[1^]: https://en.wikipedia.org/wiki/Schwarzschild_radius

To me, inside out would mean the core on the outside with the crust in the middle. ;-)