When making sampling locations, there is a lot of information out there on how to do white noise sampling, uniform sampling, uniform+jittered sampling, low discrepancy sequence sampling (eg halton) and blue noise sampling (eg mitchell's best candidate algorithm Mitchell's Best Candidate Algorithm).
For instance these, where each point is a sample location in a 2d quad. (source: https://blog.demofox.org/2017/05/29/when-random-numbers-are-too-random-low-discrepancy-sequences/)
Uniform + Jitter:
While those are good for sampling (a 2d quad in this case), here is a blue noise texture which is useful for dithering or stippling (src: http://momentsingraphics.de/?p=127)
Similarly, here is a white noise (random) one:
I've been trying to figure out in this case (a dither / stippling noise texture), if there is an equivalent to uniform sampling, uniform + jitter, or low discrepancy, and if so, what those textures might look like.
One obvious difference between the first set of the textures and the second is that the first textures take a single scalar value as input (an index) and give a 2d vector as output (a location on the 2d quad). The second set of textures takes an (x,y) 2d vector location as input, and gives out a scalar value as output.
It almost looks though like in the blue noise case that maybe you could start with the blue noise sample points, and then color every other pixel based on it's distance from the closest sample point, and that you might come up with the same image. If that's correct, could you do the same for the other flavors of sample distributions to make the other noise textures? It seems like white noise (random) wouldn't work for this though, so that doesn't seem correct.
Lastly, Jorge Jiminez has some "Interleaved Gradient Noise" that looks sort of blue noise-ish but kind of not... so seems a bit low discrepancy sequence. (http://www.iryoku.com/next-generation-post-processing-in-call-of-duty-advanced-warfare and also an image and the math mentioned here https://bartwronski.com/2016/10/30/dithering-part-three-real-world-2d-quantization-dithering/)
It makes me wonder if something about that noise shows the secret on how to generalize (low discrepancy) sample points to 2d?
Does anyone know whether there is a way to translate these sample concepts to noise textures for dithering and stippling?