Thanks for answering! I agree that in the one example image in the readme the output looks quite natural. In other implementations I've seen I could always notice "ghosts" of the Hilbert curve in the resulting image, as a subtle edge artifact. So that turned me off of the algorithm a bit, even though I find it a very elegant approach to dithering. Usually the other images were 1 bit though, that might have been a factor.
On the note of matrix based error diffusion and exploring other methods: maybe you'd enjoy Victor Ostromoukhov's variable coefficient dithering paper[0]. Instead of one diffusion matrix, it has different diffusion matrix depending on the value of the input pixel, and the result is a much more blue noise-like dithering.
Given that his paper is almost a quarter century old I've been wondering if we could find better matrices using modern solver algorithms on today's hardware. I've never used a solver myself so wouldn't know how to set this up though.
Also, there's Zhou-Fang dithering, which takes Ostromoukhov's algorithm and introduces a little bit of randomness to remove artifacts[1]. I have JavaScript implementations for both algorithms in an Observable notebook if you want to try them out[2]. It's limited to 1-bit output though.
[0] https://perso.liris.cnrs.fr/victor.ostromoukhov/publications...
[1] https://dl.acm.org/doi/abs/10.1145/1201775.882289
[2] https://observablehq.com/@jobleonard/variable-coefficient-di...