Optimal spatial sampling of light rigorously requires that identical
photoreceptors be arranged in perfectly regular arrays in two dimensions.
Examples of such perfect arrays in nature include the compound eyes of insects
and the nearly crystalline photoreceptor patterns of some fish and reptiles.
Birds are highly visual animals with five different cone photoreceptor
subtypes, yet their photoreceptor patterns are not perfectly regular. By
analyzing the chicken cone photoreceptor system consisting of five different
cell types using a variety of sensitive microstructural descriptors, we find
that the disordered photoreceptor patterns are ``hyperuniform'' (exhibiting
vanishing infinite-wavelength density fluctuations), a property that had
heretofore been identified in a unique subset of physical systems, but had
never been observed in any living organism. Remarkably, the photoreceptor
patterns of both the total population and the individual cell types are
simultaneously hyperuniform. We term such patterns ``multi-hyperuniform''
because multiple distinct subsets of the overall point pattern are themselves
hyperuniform. We have devised a unique multiscale cell packing model in two
dimensions that suggests that photoreceptor types interact with both short- and
long-ranged repulsive forces and that the resultant competition between the
types gives rise to the aforementioned singular spatial features characterizing
the system, including multi-hyperuniformity.Comment: 31 pages, 12 figure
