Except that's mathematically generated totally random noise, not the
type of noise we see from a bayer sensor.
That's true, but the noise from a sensor is a lot closer to mathematically-generated noise than you think, in character; you seem to be getting your idea of what a sensor generates from
conversions . Conversions filter out noise near the nyquist through demosaicing and NR. All converters use significant NR even when you turn NR "Off" - all that "off" means is that the least amount of NR that the converter wants you to see is used. All RAW data is much noisier than you seem to think.
When you take your converted grey patches and resample them, you are resampling data that has almost nothing near the nyquist, despite the fact that this is where the RAW noise is concentrated. Then, when you look at the standard deviations, they are meaningless because standard deviations of different samples are only comparable at the pixel level when the spectral distribution of noise is the same.
I just took a patch of sky from a converted RAW, and resampled it to 25%, 50%, 200%, and 400%, and laid them out in order across the screen (with the original in the middle). I could clearly see that the visible pixel-level noise increased a good amount, going from left to right, between each neighbor. The standard deviations of all were within a very narrow range; 8.56 for the 25%, and 8.71 for the 400%:
When your eyes clearly show you that noise at the new 100% is much different, and the standard deviations are the same, it is very clear that standard deviations are irrelevant in the context. The standard deviation of an image sample is
NOT a measure of its noise, either at the pixel level, or at the image level. Spectral distributions are much better for those, considering pixel and image frequency, respectively.
Now, when the pro-high-density theorists here are measuring noise with standard deviation, they are almost always talking about real undemosaiced RAW noise, concentrated at the nyquist (where standard deviation is more meaningful); not reduced, correlated, converted noise.
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John