One oddity of Lorentz invariance is that two non-parallel boosts decompose into a boost and spatial rotation.

I've never quite wrapped my head around this and was hoping to get some insight from this simulation. But afaict, I'm not seeing this effect (press W for a bit, the A for a bit and it's not obvious I'm at a different orientation - if I look down at the ground the gridlines are still axial).

I don't know if I'm misinterpreting the math, or the simulation, or maybe the simulation is doing something to 'correct' for this behavior so things are more natural, or something else. Does anyone have any insight?