Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem

Abstract

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.

31 pages, 12 figures

References in corpus (17)

• Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond
• Local Density Fluctuations, Hyperuniformity, and Order Metrics
• Designer disordered materials with large complete photonic band gaps
• Unexpected Density Fluctuations in Jammed Disordered Sphere Packings
• Isotropic Band Gaps and Freeform Waveguides Observed in Hyperuniform Disordered Photonic Solids
• Hyperuniformity in point patterns and two-phase random heterogeneous media
• Random Sequential Addition of Hard Spheres in High Euclidean Dimensions
• Classical Disordered Ground States: Super-Ideal Gases, and Stealth and Equi-Luminous Materials
• Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings
• Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory
• Suppressed compressibility at large scale in jammed packings of size disperse spheres
• Experimental study of random close packed colloidal particles
• Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres
• Anomalous local coordination, density fluctuations, and void statistics in disordered hyperuniform many-particle ground states
• Generation of Primordial Cosmological Perturbations from Statistical Mechanical Models
• Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. II. Anisotropy in particle shape
• Direct laser writing of three dimensional network structures as templates for disordered photonic materials

Cited by in corpus (109)

• Hyperuniform States of Matter
• Non-Equilibrium Strongly Hyperuniform Fluids of Circle Active Particles with Large Local Density Fluctuations
• Hyperuniformity and its Generalizations
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• Ensemble Theory for Stealthy Hyperuniform Disordered Ground States
• Hyperuniform density fluctuations and diverging dynamic correlations in periodically driven colloidal suspensions
• Basic Understanding of Condensed Phases of Matter via Packing Models
• Circular swimming motility and disordered hyperuniform state in an algae system
• Effective interactions and large deviations in stochastic processes
• Designing Disordered Hyperuniform Two-Phase Materials with Novel Physical Properties
• Hyperuniformity of Quasicrystals
• Perspective: Inverse methods for material design
• Ultrafast jamming of electrons into an amorphous entangled state
• Random Scalar Fields and Hyperuniformity
• Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations
• Stone-Wales Defects Preserve Hyperuniformity in Amorphous Two-Dimensional Materials
• Disordered Hyperuniform Heterogeneous Materials
• Hyperuniform Active Chiral Fluids with Tunable Internal Structure
• Large-scale structure and hyperuniformity of amorphous ices
• Hyperuniform monocrystalline structures by spinodal solid-state dewetting
• Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra
• Nonlocal Effective Electromagnetic Wave Characteristics of Composite Media: Beyond the Quasistatic Regime
• Enhanced Pinning For Vortices in Hyperuniform Substrates and Emergent Hyperuniform Vortex States
• Generalized stealthy hyperuniform processes : maximal rigidity and the bounded holes conjecture
• Ground states of stealthy hyperuniform potentials. II. Stacked-slider phases
• Hidden Multiscale Order in the Primes
• New Tessellation-Based Procedure to Design Perfectly Hyperuniform Disordered Dispersions for Materials Discovery
• Microscopic theory for hyperuniformity in two-dimensional chiral active fluid
• Large-scale structure of randomly jammed particles
• Disordered hyperuniformity in two-component non-additive hard disk plasmas
• The random packing density of nearly spherical particles
• Nearly hyperuniform, nonhyperuniform, and antihyperuniform density fluctuations in two-dimensional transition metal dichalcogenides with defects
• Methodology to Construct Large Realizations of Perfectly Hyperuniform Disordered Packings
• Quantum phase transition between hyperuniform density distributions
• Effective Elastic Wave Characteristics of Composite Media
• Equation of state of polydisperse hard-disk mixtures in the high-density regime
• Uncovering Multiscale Order in the Prime Numbers via Scattering
• Hyperuniformity of generalized random organization models
• Hyperuniform point sets on the sphere: deterministic constructions
• Disordered multihyperuniformity derived from binary plasmas
• Characterization of Maximally Random Jammed Sphere Packings. III. Transport and Electromagnetic Properties via Correlation Functions
• Theoretical Prediction of the Effective Dynamic Dielectric Constant of Disordered Hyperuniform Anisotropic Composites Beyond the Long-Wavelength Regime
• Large deviations and optimal control forces for hard particles in one dimension
• Confined disordered strictly jammed binary sphere packings
• A geometric-Structure Theory for maximally Random Jammed Packings
• Effect of Window Shape on the Detection of Hyperuniformity via the Local Number Variance
• Dynamic Measure of Hyperuniformity and Nonhyperuniformity in Heterogeneous Media via the Diffusion Spreadability
• Disordered Hyperuniform Quasi-1D Materials
• Disordered hyperuniformity in superconducting vortex lattices
• Hyperuniformity in cyclically driven glasses
• Anisotropic suppression of hyperuniformity of elastic systems in media with planar disorder
• Extraordinary Optical and Transport Properties of Disordered Stealthy Hyperuniform Two-Phase Media
• Hidden Order Beyond Hyperuniformity in Critical Absorbing States
• Motility Induced Phase Separation and Frustration in Active Matter Swarmalators
• Optimized Large Hyperuniform Binary Colloidal Suspensions in Two Dimensions
• Non-equilibrium dynamic hyperuniform states
• Inverse design of disordered stealthy hyperuniform spin chains
• Correlations and hyperuniformity in the avalanche size of the Oslo Model
• Structural characterization and statistical-mechanical model of epidermal patterns
• The structure factor of primes
• Anomalous suppression of large-scale density fluctuations in classical and quantum spin liquids
• Characterizing the Hyperuniformity of Ordered and Disordered Two-Phase Media
• Information Content of Hierarchical n-Point Polytope Functions for Quantifying and Reconstructing Disordered Systems
• Subdiffusive light transport in three-dimensional subrandom arrays
• Persistent homology and topological statistics of hyperuniform point clouds
• A minimal statistical-mechanical model for multihyperuniform patterns in avian retina
• Hyperuniformity Order Metric of Barlow Packings
• Hyperuniform Jammed Sphere Packings Have Anomalous Material Properties
• Hyperuniformity on spherical surfaces
• Hyperuniformity and conservation laws in non-equilibrium systems
• Local order metrics for many-particle systems across length scales
• How does a hyperuniform fluid freeze?
• Characterizing Pixel and Point Patterns with a Hyperuniformity Disorder Length
• Fluctuation and Entropy in Spectrally Constrained random fields
• Quantifying the Long-Range Structure of Foams and Other Cellular Patterns with Hyperuniformity Disorder Length Spectroscopy
• Hyperuniform Density Distributions of Brownian Particles via Designer External Potentials
• Hyperuniform states generated by a critical friction field
• Hyperuniform interfaces in non-equilibrium phase coexistence
• Hyperuniformity in two-dimensional periodic and quasiperiodic point patterns
• Dynamical properties of particulate composites derived from ultradense stealthy hyperuniform sphere packings
• Dynamical phase transitions in one-dimensional hard-particle systems
• Existence of Nonequilibrium Glasses in the Degenerate Stealthy Hyperuniform Ground-State Manifold
• Geometrical properties of mechanically annealed systems near the jamming transition
• A local orientational order parameter for systems of interacting particles
• Correlations in interacting electron liquids: Many-body statistics and hyperuniformity
• Hyperuniform properties of the square-triangle tilings
• Vectorial active matter on the lattice: polar condensates and nematic filaments
• Hyperuniformity Disorder Length Spectroscopy for Extended Particles
• Hyperdisordered cell packing on a growing surface
• Effective delocalization in the one-dimensional Anderson model with stealthy disorder
• Nearest-Neighbor Functions for Disordered Stealthy Hyperuniform Many-Particle Systems
• Impact of Random Spatial Truncation and Reciprocal-Space Binning on the Detection of Hyperuniformity in Disordered Systems
• Quantifying when hyperuniformity of a many-particle system leads to uniformity across length scales
• Percolation of systems having hyperuniformity or giant number-fluctuations
• Threshold Response to Stochasticity in Morphogenesis
• Hyperuniformity in Ashkin-Teller model
• Inferring traits of hyperuniformity from local structures via persistent homology
• Hyperuniformity of Weighted Particle Systems
• Diverse patterns of pebbles on sand on Mars and Earth
• Anti-hyperuniform diluted vortex matter induced by correlated disorder
• Spectral Leakage and Masking Effects in the Measurement of Hyperuniformity
• Theoretical Basis for Classifying Hyperuniform States of Two-Component Systems
• Hyperuniformity near jamming transition over a wide range of bidispersity
• Conductance fluctuations in random resistor networks with hyperuniform disorder
• Impact of Stealthy Hyperuniform Magnetic Impurity Configurations on Bulk Magnetism in a Two-dimensional Heisenberg Model
• Topological Defects, Inherent Structures, and Hyperuniformity
• Hyperuniform patterns nucleated at low temperatures: Insight from vortex matter imaged in unprecedentedly large fields-of-view
• Random matrix statistics and safety rest areas on interstates in the United States
• Precise Determination of the Long-Time Asymptotics of the Diffusion Spreadability of Two-Phase Media