The first inspiration: If a catbox could be made to shake, would it automatically cover the crap? Common sense says, heavy stuff falls right? So the litter, as it’s thrown side to side, would fly on top, and, presto, Sea of Tranquility.

Makes for a funny image (which I’d draw if I had time) of a covered box on springs with a bewildered feline sticking her face out. Or maybe it could be motorized.
Problem is (I think) that actually common sense is wrong: Larger pieces rise, because small stuff falls into the smaller gaps and winds up on the bottom. Happens all the time to breakfast cereal. So, what if the pieces of litter were like really big flakes? Probably would freak the cat from using it and still wouldn’t work. What’s the answer? An agitator like a washing machine? (Yeah, that’s real low tech.) Springs that cause twisting? A sensor that, after it detects a cat departing, kind of clamshells up with box then reopens? What’s your idea?

Here’s another cat-related post: Cat Food Topping. And it features one of my daughter’s cartoons.