>I wouldn't have thought Nearest would be the correct interpolant, but like I said, I don't have good intuition here. What's the logic for using Nearest instead of Linear?

it's that, at least how I understood the `InterpolatedImage` worked, that this would be the interpolant choice that corresponded to a set of delta functions convolved with pixels to make a 2D pixel grid - this is what I think we need to correspond to the `UncorrelatedNoise`... But if this were the correct understanding I would expect the "pixel grid" to rotate as well, from what I'm seeing above this doesn't seem to be how the interpolant is working.  I'm going to try a quick test...

>OK, thinking about it a bit, I guess if the CF is uncorrelated, then Nearest would match my Pixel representation, so that could make sense. Or maybe your investigation here is evidence that my thought of using Pixel for UCF is wrong.

Np, I think the pixel for the UCF is right, so it's a generalization of the Pixel representation to a 2D lookup table that is why I'm thinking Nearest ought to be the correct option.

>Interestingly, if I change the interpolant to anything besides Linear (I tried Nearest, Cubic, Quintic, Lanczos 5, and 7), it also fails. So perhaps this might be a case of the test passing by a bit of luck. It seems unlikely to me the Linear is so precisely the correct interpolant that nothing else works correctly. Maybe we just got lucky with the rng choice or something.

>(I checked this last possibility by changing the rseed value from 12345 to 1234567, and there were two failures, but not this one. Using rseed=0 (to use the time) and running a bunch of times, it didn't fail for me, so maybe that idea is a red herring.)

In truth, I think the tests are rather subject to noise, especially some of the small image tests (which examine basic things like the variance).  for some of the more involved had to make quite large images to get them to pass, and it was becoming very time consuming, so there was always a little balancing going on.

I also agree that it seems unlikely to me the Linear is so precisely the correct interpolant that nothing else works correctly, but I think it is quite well behaved in both real and Fourier space (~ sinc^2) and this does make a difference to the stability.  but the bottom line of this stuff is that it is tricky, and I cannot discount the possibility of there still being slight imperfections that are yet to be understood (as I found above I'm still learning about what assuiptions are valid!)