https://gist.github.com/vjeranc/265db912d4004c7c0b0f16ae5fda...
Interestingly, sphere is not infinite so having this aperiodic tiling is pointless (still looks nice).
Although, I never found out if there's a similar set of tiles (or a monotile) that can tile an infinite cone.
For physical tiles, clearly not as the curvature would be wrong. I'm sure there remain interesting questions, but it's not sufficiently obvious to me what projection makes sense that I'm able to get further into the problem.
What you wrote is of course right as well
Assuming it's possible at all, I think scale winds up mattering in a way that it doesn't for a plane, because you have to accommodate "meeting yourself" again some fixed distance away.
vec2 st = (vUv.xy * h + time/100. + 1.);
The tiling is not infinite, it's inside a big triangle, so with enough time you will travel outside of it, but I guess with proper bounds you can move around or make the triangle bigger.
vec2 st = (vUv.xy * h/(1.+0.5*cos(time)) + time/100. + 1.);