In a homogeneous mixture, at some scale, you can still find clumping - after all, if the elements of the mixture are randomly distributed, why wouldn't you? Whereas, in a hyperuniform mixture, there is no clumping.

A computer-scientific analogy would be sequences of random numbers. A sequences of bits can be perfectly random and still contain a hundred zeroes in a row. Whereas if you had a sequences of a billion bits which never had a run of a hundred zeroes, you could be pretty sure that it wasn't random.

You can measure this with metrics like the Ripley K:

http://wiki.landscapetoolbox.org/doku.php/spatial_analysis_m...

Before i was a programmer, i was a cell biologist. A colleague was studying CCR5, a cell-surface receptor that is involved in HIV entry into cells. She used electron microscopy with a rather tricky "rip-off" preparation [1] to look at the spatial distribution of CCR5 in cell membranes. One of the things she observed was that the receptors were remarkably evenly spaced. Being slightly more computationally inclined than her, i did some reading, came across the Ripley K metric, and wrote some Python scripts to analyse the distribution of receptors in her images. Lo and behold, they were indeed dispersed, suggesting that there was some cellular mechanism pushing the receptors apart. It turned out that the spacing wasn't actually very interesting to her, it was just a curiosity she'd noticed, so it was a complete waste of time really. Anyway, that was back in 2005. I'm glad these chicken eyeball bods have finally caught up, but it doesn't seem like a massive revelation.

[1] https://www.ncbi.nlm.nih.gov/pubmed/1906908