For some reason I became temporarily obsessed with creating very uniform deterministic noise.
This was my best attempt :
All the grayscale values present here follow an uniform distribution from 0 to 255.
I obtained it by automatically placing points one by one from darkest to lightest as far as possible from each other.
Distances were weighted depending on the brightness difference and then summed (similar pixels need to be further).
The computed distances warp on a horizontal and vertical basis.
I did this in a very naive way without checking any existing documentation about this.
It took a few hours for my computer to generate this 128x128 texture this way.
And for you to compare here it is next to a regular random noise :
Here are other funny pictures I obtained while making various related tests :