The reported article:
Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem
The 30 year old article
Science 22 July 1983:
Vol. 221 no. 4608 pp. 382-385
DOI: 10.1126/science.6867716
REPORTS
Spectral consequences of photoreceptor sampling in the rhesus retina
"...a novel spatial sampling principle that introduces minimal noise for spatial frequencies below the Nyquist limits implied by local receptor densities, while frequencies above the nominal Nyquist limits are not converted into conspicuous moire patterns, but instead are scattered into broadband noise. This sampling scheme allows the visual system to escape aliasing distortion..."
The pattern discovered in 1983 was called a "Poisson Disk". It allows cell centers to be randomly (Poisson) distributed within a circle of radius r, but never approaching closer than some minimum r.
This discovery was the basis of a lot of psuedo-random dither algorithms that are still used in computer graphics.
-----------
Scrape away the jargon, and "disordered hyperuniformity" sounds a lot like "Poisson disk"