For some reason I became temporarily obsessed with creating very uniform deterministic noise.

This was my best attempt :

result 17

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.
At some point I should redo it with precise grey values rather than useless 24bit color values.

And for you to compare here it is next to a regular random noise :

result 17 normal Noise To Compare To

Here are other funny pictures I obtained while making various related tests :

result 01
result 02
result 03
result 04
result 05
result 06
result 07
result 08
result 09
result 10
result 11
result 12
result 13
result 14
result 15