I still like snowflakes for this: https://levien.com/snowflake-explain.html is a half-finished blog post explaining the motivation and algorithm I came up with. I never did careful user testing, but suspect that the answer would be that some people can reliably distinguish the patterns, others won't be able to.

In any case, there are a lot of variations on this "visual hash" idea, including the original fractal one, and I heard of more recent work to use the hash to seed StyleGAN face generation.