Birds are known for their extremely acute sense of vision. The very peculiar
structural distribution of five different types of cones in the retina
underlies this exquisite ability to sample light. It was recently found that
each cone population as well as their total population display a disordered
pattern in which long wave-length density fluctuations vanish. This property,
known as hyperuniformity is also present in perfect crystals. In situations
like the avian retina in which both the global structure and that of each
component display hyperuniformity, the system is said to be multi-hyperuniform.
In this work, we aim at devising a minimal statistical-mechanical model that
can reproduce the main features of the spatial distribution of photoreceptors
in avian retina, namely the presence of disorder, multi-hyperuniformity and
local hetero-coordination. This last feature is key to avoid local clustering
of the same type of photoreceptors, an undesirable feature for the efficient
sampling of light. For this purpose we formulate a simple model that
definitively exhibits the required structural properties, namely an equimolar
three-component mixture (one component to sample each primary color, red,
green, and blue) of non-additive hard disks to which a long-range logarithmic
repulsion is added between like particles. A Voronoi analysis of our idealized
system of photoreceptors shows that the space-filling Voronoi polygons
interestingly display a rather uniform area distribution, symmetrically
centered around that of a regular lattice, a structural property also found in
human retina. Disordered multi-hyperuniformity offers an alternative to
generate photoreceptor patterns with minimal long-range concentration and
density fluctuations. This is the key to overcome the difficulties in devising
an efficient visual system in which crystal-like order is absent