# Universality of Form: The Case of Retinal Cone Photoreceptor Mosaics

## Abstract

**:**

## 1. Introduction

## 2. Entropy Maximization

## 3. Spatial Distributions of Cone Photoreceptors in the Retinas of Vertebrates

#### 3.1. Spatial Distributions of Human Cone Photoreceptors

#### 3.2. Spatial Distributions of Vertebrate Cone Photoreceptors: From Rodent to Bird

#### 3.3. Bounds on Retinal Coldness

## 4. Lemaître’s Law

#### 4.1. Human Cone Mosaics

#### 4.2. Vertebrate Cone Mosaics: From Rodent to Bird

## 5. Concluding Remarks

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Jaynes, E.T. Information Theory and Statistical Mechanics. Phys. Rev.
**1957**, 106, 620–630. [Google Scholar] [CrossRef] - Jaynes, E.T. Information Theory and Statistical Mechanics. II. Phys. Rev.
**1957**, 108, 171–190. [Google Scholar] [CrossRef] - Caticha, A. Lectures on Probability, Entropy, and Statistical Physics. arXiv
**2008**, arXiv:0808.0012. [Google Scholar] - Banavar, J.R.; Maritan, A.; Volkov, I. Applications of the principle of maximum entropy: From physics to ecology. J. Phys. Condens. Matter
**2010**, 22, 063101. [Google Scholar] [CrossRef] [PubMed] - Mora, T.; Walczak, A.M.; Bialek, W.; Callan, C.G. Maximum entropy models for antibody diversity. Proc. Natl. Acad. Sci. USA
**2010**, 107, 5405–5410. [Google Scholar] [CrossRef] [PubMed] - Harte, J.; Zillio, T.; Conlisk, E.; Smith, A.B. Maximum Entropy and the State-Variable Approach to Macroecology. Ecology
**2008**, 89, 2700–2711. [Google Scholar] [CrossRef] - Berger, A.L.; Della Pietra, V.J.; Della Pietra, S.A. A Maximum Entropy Approach to Natural Language Processing. Comput. Linguist.
**1996**, 22, 39–71. [Google Scholar] - Landauer, R. Nonlinearity, multistability, and fluctuations: Reviewing the reviewers. Am. J. Physiol.
**1981**, 241, R107–R113. [Google Scholar] [CrossRef] - Caticha, A.; Preuss, R. Maximum entropy and Bayesian data analysis: Entropic prior distributions. Phys. Rev. E
**2004**, 70, 046127. [Google Scholar] [CrossRef] - Erickson, G.J.; Rychert, J.T.; Smith, C.R. (Eds.) Maximum Entropy and Bayesian Methods; Springer: Dordrecht, The Netherlands, 1998. [Google Scholar]
- Linden, W.; Dose, V.; Fischer, R.; Preuss, R. (Eds.) Maximum Entropy and Bayesian Methods; Springer: Dordrecht, The Netherlands, 1999. [Google Scholar]
- Palmieri, F.A.N.; Ciuonzo, D. Objective priors from maximum entropy in data classification. Inf. Fusion
**2013**, 14, 186–198. [Google Scholar] [CrossRef] - Barua, A.; Beygi, A.; Hatzikirou, H. Close to Optimal Cell Sensing Ensures the Robustness of Tissue Differentiation Process: The Avian Photoreceptor Mosaic Case. Entropy
**2021**, 23, 867. [Google Scholar] [CrossRef] [PubMed] - Wässle, H.; Riemann, H.J. The mosaic of nerve cells in the mammalian retina. Proc. R. Soc. Lond. B Biol. Sci.
**1978**, 200, 441–461. [Google Scholar] [PubMed] - Peichl, L. Diversity of Mammalian Photoreceptor Properties: Adaptations to Habitat and Lifestyle? Anat. Rec. A Discov. Mol. Cell. Evol. Biol.
**2005**, 287, 1001–1012. [Google Scholar] [CrossRef] [PubMed] - Viets, K.; Eldred, K.C.; Johnston, R.J. Mechanisms of Photoreceptor Patterning in Vertebrates and Invertebrates. Trends Genet.
**2016**, 32, 638–659. [Google Scholar] [CrossRef] - Costa, L.F.; Rocha, F.; Lima, S.M.A. Statistical mechanics characterization of neuronal mosaics. Appl. Phys. Lett.
**2005**, 86, 093901. [Google Scholar] [CrossRef] - Mehri, A. Non-extensive distribution of human eye photoreceptors. J. Theor. Biol.
**2017**, 419, 305–309. [Google Scholar] [CrossRef] - Lemaître, J.; Gervois, A.; Troadec, J.P.; Rivier, N.; Ammi, M.; Oger, L.; Bideau, D. Arrangement of cells in Voronoi tessellations of monosize packing of discs. Philos. Mag. B
**1993**, 67, 347–362. [Google Scholar] [CrossRef] - Gervois, A.; Troadec, J.P.; Lemaître, J. Universal properties of Voronoi tessellations of hard discs. J. Phys. A Math. Gen.
**1992**, 25, 6169–6177. [Google Scholar] [CrossRef] - Thompson, D.W. On Growth and Form, 2nd ed.; Cambridge University Press: Cambridge, UK, 1963. [Google Scholar]
- Farhadifar, R.; Röper, J.C.; Aigouy, B.; Eaton, S.; Jülicher, F. The Influence of Cell Mechanics, Cell-Cell Interactions, and Proliferation on Epithelial Packing. Curr. Biol.
**2007**, 17, 2095–2104. [Google Scholar] [CrossRef] - Ball, P. In retrospect: On Growth and Form. Nature
**2013**, 494, 32–33. [Google Scholar] [CrossRef] - Pathria, R.K.; Beale, P.D. Statistical Mechanics, 3rd ed.; Elsevier: New York, NY, USA, 2011. [Google Scholar]
- Coles, P. From Cosmos to Chaos: The Science of Unpredictability; Oxford University Press: Oxford, UK, 2006. [Google Scholar]
- Jaynes, E.T. Probability Theory: The Logic of Science; Cambridge University Press: Cambridge, UK, 2003. [Google Scholar]
- Haegeman, B.; Etienne, R.S. Entropy Maximization and the Spatial Distribution of Species. Am. Nat.
**2010**, 175, E74–E90. [Google Scholar] [CrossRef] [PubMed] - Roorda, A.; Williams, D.R. The arrangement of the three cone classes in the living human eye. Nature
**1999**, 397, 520–522. [Google Scholar] [CrossRef] [PubMed] - Chalupa, L.M.; Finlay, B.L. (Eds.) Development and Organization of the Retina: From Molecules to Function; Plenum Press: New York, NY, USA, 1998. [Google Scholar]
- Kram, Y.A.; Mantey, S.; Corbo, J.C. Avian Cone Photoreceptors Tile the Retina as Five Independent, Self-Organizing Mosaics. PLoS ONE
**2010**, 5, e8992. [Google Scholar] [CrossRef] - Schmauder, S.; Mishnaevsky, L. Micromechanics and Nanosimulation of Metals and Composites: Advanced Methods and Theoretical Concepts; Springer: Berlin/Heidelberg, Germany, 2009. [Google Scholar]
- Wand, M.P. Data-Based Choice of Histogram Bin Width. Am. Stat.
**1997**, 51, 59–64. [Google Scholar] - Scott, D.W. On optimal and data-based histograms. Biometrika
**1979**, 66, 605–610. [Google Scholar] [CrossRef] - Rocha, F.A.; Ahnelt, P.K.; Peichl, L.; Saito, C.A.; Silveira, L.C.; De Lima, S.M. The topography of cone photoreceptors in the retina of a diurnal rodent, the agouti (Dasyprocta aguti). Vis. Neurosci.
**2009**, 26, 167–175. [Google Scholar] [CrossRef] - Klein, D.; Mendes-Madeira, A.; Schlegel, P.; Rolling, F.; Lorenz, B.; Haverkamp, S.; Stieger, K. Immuno-Histochemical Analysis of Rod and Cone Reaction to RPE65 Deficiency in the Inferior and Superior Canine Retina. PLoS ONE
**2014**, 9, e86304. [Google Scholar] [CrossRef] - Roorda, A.; Metha, A.B.; Lennie, P.; Williams, D.R. Packing arrangement of the three cone classes in primate retina. Vis. Res.
**2001**, 41, 1291–1306. [Google Scholar] [CrossRef] - Allison, W.T.; Barthel, L.K.; Skebo, K.M.; Takechi, M.; Kawamura, S.; Raymond, P.A. Ontogeny of cone photoreceptor mosaics in zebrafish. J. Comp. Neurol.
**2010**, 518, 4182–4195. [Google Scholar] [CrossRef] - Pei, Y.; Biswas, S.; Fussell, D.S.; Pingali, K. An elementary introduction to Kalman filtering. Commun. ACM
**2019**, 62, 122–133. [Google Scholar] [CrossRef] - Sadoc, J.F.; Rivier, N. (Eds.) Foams and Emulsions; Springer: Dordrecht, The Netherlands, 1999. [Google Scholar]
- Miklius, M.P.; Hilgenfeldt, S. Analytical Results for Size-Topology Correlations in 2D Disk and Cellular Packings. Phys. Rev. Lett.
**2012**, 108, 015502. [Google Scholar] [CrossRef] [PubMed] - Morley, D.O.; Thorneywork, A.L.; Dullens, R.P.A.; Wilson, M. Generalized network theory of physical two-dimensional systems. Phys. Rev. E
**2020**, 101, 042309. [Google Scholar] [CrossRef] [PubMed] - Carter, R.; Sánchez-Corrales, Y.E.; Hartley, M.; Grieneisen, V.A.; Marée, A.F.M. Pavement cells and the topology puzzle. Development
**2017**, 144, 4386–4397. [Google Scholar] [CrossRef] - Xuan, B.; Whitaker, O.; Wilson, M. The network structure of the corneal endothelium. J. Chem. Phys.
**2023**, 158, 055101. [Google Scholar] [CrossRef] [PubMed] - Le Caër, G.; Delannay, R. Correlations in topological models of 2D random cellular structures. J. Phys. A Math. Gen.
**1993**, 26, 3931–3954. [Google Scholar] [CrossRef] - Cerisier, P.; Rahal, S.; Rivier, N. Topological correlations in Bénard–Marangoni convective structures. Phys. Rev. E
**1996**, 54, 5086–5094. [Google Scholar] [CrossRef] - Castro, M.; Cuerno, R.; García-Hernández, M.M.; Vázquez, L. Pattern-Wavelength Coarsening from Topological Dynamics in Silicon Nanofoams. Phys. Rev. Lett.
**2014**, 112, 094103. [Google Scholar] [CrossRef] - Morley, D.O.; Wilson, M. Constructing bilayers with tuneable ring statistics and topologies. Mol. Phys.
**2019**, 117, 3148–3157. [Google Scholar] [CrossRef] - Le Caër, G. Topological models of cellular structures. J. Phys. A Math. Gen.
**1991**, 24, 1307–1317. [Google Scholar] [CrossRef] - Lewis, F.T. The correlation between cell division and the shapes and sizes of prismatic cells in the epidermis of cucumis. Anat. Rec.
**1928**, 38, 341–376. [Google Scholar] [CrossRef] - Knessl, C. Integral representations and asymptotic expansions for Shannon and Renyi entropies. Appl. Math. Lett.
**1998**, 11, 69–74. [Google Scholar] [CrossRef] - MathOverflow. Available online: https://mathoverflow.net/q/397422 (accessed on 13 July 2021).
- Delannay, R.; Le Caër, G. Topological Characteristics of 2D Cellular Structures Generated by Fragmentation. Phys. Rev. Lett.
**1994**, 73, 1553–1556. [Google Scholar] [CrossRef] - Boulatov, D.V.; Kazakov, V.A.; Kostov, I.K.; Migdal, A.A. Analytical and numerical study of a model of dynamically triangulated random surfaces. Nucl. Phys. B
**1986**, 275, 641–686. [Google Scholar] [CrossRef] - Godrèche, C.; Kostov, I.; Yekutieli, I. Topological Correlations in Cellular Structures and Planar Graph Theory. Phys. Rev. Lett.
**1992**, 69, 2674–2677. [Google Scholar] [CrossRef] [PubMed] - Fortes, M.A. Applicability of the Lewis and Aboav–Weaire laws to 2D and 3D cellular structures based on Poisson partitions. J. Phys. A Math. Gen.
**1995**, 28, 1055–1068. [Google Scholar] [CrossRef] - Grünbaum, B.; Shephard, G.C. Tilings and Patterns, 2nd ed.; Dover Publications: New York, NY, USA, 2016. [Google Scholar]
- Duyckaerts, C.; Godefroy, G. Voronoi tessellation to study the numerical density and the spatial distribution of neurones. J. Chem. Neuroanat.
**2000**, 20, 83–92. [Google Scholar] [CrossRef] [PubMed] - Zhang, F.; Kurokawa, K.; Lassoued, A.; Crowell, J.A.; Miller, D.T. Cone photoreceptor classification in the living human eye from photostimulation-induced phase dynamics. Proc. Natl. Acad. Sci. USA
**2019**, 116, 7951–7956. [Google Scholar] [CrossRef] - Oppenheim, I. Book Review: The Maximum Entropy Formalism. J. Stat. Phys.
**1980**, 23, 127. [Google Scholar] [CrossRef]

**Figure 1.**Spatial distributions of cone photoreceptors in a living human nasal retina, at one degree of eccentricity. The image, in the top-left corner with the scale bar = 5 µm, is adapted with permission from [28]. Copyright 1999, Springer Nature. Figures in the bottom row, from left to right, illustrate short-, medium-, and long-wavelength-sensitive cones separately.

**Figure 2.**The (

**left panel**) shows the blue cone photoreceptors in a living human retina. Searching for the nearest neighbors is depicted in the (

**right panel**).

**Figure 3.**Nearest-neighbor-distance distributions of cone photoreceptors in a living human retina. The colors of the histograms correspond to their respective cone subtypes. Values of mean and standard deviation in micrometers for each distribution read ${\mu}_{b}=3.572$, ${\sigma}_{b}=1.020$, ${\mu}_{g}=1.188$, ${\sigma}_{g}=0.300$, ${\mu}_{r}=1.172$, and ${\sigma}_{r}=0.257$.

**Figure 4.**Kullback–Leibler divergence is depicted as a function of $\beta $ in the (

**left panel**), where it has the global minimum of $0.001$ at $\beta =1.284$. The (

**right panel**) shows a comparison between the in vivo observed frequencies of appearance of cone photoreceptors in a human retina and the predictions of the theory (5) for $\beta =1.284$. The color of each bar corresponds to its respective cone subtype.

**Figure 5.**The image in the top-left corner (scale bar = 50 µm) illustrates the spatial distribution of cone photoreceptors in the dorsal mid-peripheral retina of a diurnal rodent called the agouti. It is adapted with permission from [34]. Copyright 2009, Cambridge University Press. In this image, the short-wavelength-sensitive-cone opsin is represented as green and the long-wavelength-sensitive-cone opsin as violet; next to it, in the digitized image, we have reversed the colors. Nearest-neighbor-distance distributions in the third row have the entropies of ${h}_{v}=3.310$ and ${h}_{g}=1.787$; next to them, we have shown a comparison between the experimental observation of cone ratios in the agouti retina and the predictions of the theory (5) evaluated at the global minimum of the Kullback–Leibler divergence, that is, $\beta =1.310$. The colors of the histograms and the bar chart correspond to their respective cone subtypes.

**Figure 6.**The image in the top-left corner, adapted from [35], shows the spatial distribution of cone photoreceptors in the inferior peripheral retina of a dog; the short-wavelength-sensitive-cone opsin is represented as green and the long-/medium-wavelength-sensitive-cone opsin as red. The entropies of the NND distributions in the third row read ${h}_{g}=3.933$ and ${h}_{r}=2.440$. The colors of the histograms correspond to their respective cone subtypes. Next to the NND distributions, we have shown a comparison between the experimental observation of cones’ frequencies of appearance and the predictions of the theory for $\beta =1.127$.

**Figure 7.**The image in the top-left corner, which shows the spatial distribution of cone photoreceptors in the nasal retina of a monkey (macaque), is provided by A. Roorda, adapted with permission from [36]. Copyright 2001, Elsevier. Short-, medium-, and long-wavelength-sensitive cones are depicted as blue, green, and red points, respectively. The entropies of the NND distributions of cone subtypes, shown in the third row, read ${h}_{b}=1.019$, ${h}_{g}=0.018$, and ${h}_{r}=-0.476$. The predictions of the theory, illustrated in the fourth row, are evaluated at $\beta =1.174$. The colors of the histograms and the bar chart correspond to their respective cone subtypes.

**Figure 8.**The image in the top-left corner, provided by A. Roorda, illustrates the spatial distribution of cone photoreceptors in the temporal retina of a human. The image is adapted with permission from [36]. Copyright 2001, Elsevier. Blue, green, and red points represent the short-, medium-, and long-wavelength-sensitive cones, respectively. The entropies of the NND distributions of cone subtypes in the third row are ${h}_{b}=2.977$, ${h}_{g}=1.691$, and ${h}_{r}=0.651$. The colors of the histograms correspond to their respective cone subtypes. The theoretical predictions are shown in the last row, where $\beta =1.291$.

**Figure 9.**The image in the top-left corner shows the spatial distribution of cone photoreceptors in the retina of the zebrafish. The image is adapted with permission from [37]. Copyright 2010, John Wiley and Sons. Blue-, UV-, red-, and green-sensitive cones are depicted as points with their respective colors. The entropies of the NND distributions of cone subtypes in the third and fourth rows are ${h}_{b}=1.471$, ${h}_{\mathrm{UV}}=1.440$, ${h}_{r}=1.350$, and ${h}_{g}=1.128$. The theoretical predictions are evaluated at $\beta =1.894$. The colors of the histograms and the bar chart correspond to their respective cone subtypes.

**Figure 10.**The digitized image of the spatial distribution of cone photoreceptors in the dorsal nasal retina of the chicken, shown in the top-left corner, is constructed from the data reported in [30]. Violet-, blue-, red-, and green-sensitive cones are represented as points with their respective colors; double cones are shown as white. The entropies of the NND distributions of cone subtypes in the third and fourth rows read ${h}_{v}=2.291$, ${h}_{b}=2.081$, ${h}_{r}=1.826$, ${h}_{g}=1.739$, and ${h}_{d}=1.364$. The colors of the histograms correspond to their respective cone subtypes. The predictions of the theory are evaluated at $\beta =1.527$.

**Figure 11.**In the (

**left panel**), the dashed blue and yellow curves correspond to ${\mu}_{2}{p}_{6}^{2}=1/2\pi $ and ${\mu}_{2}+{p}_{6}=1$, respectively. The red points are obtained from (14), subjected to the constraint $\u2329n\u232a=6$. This plot suggests that the known lower bound of (16) can be relaxed to $0.27$. The (

**right panel**) presents a comparison between the analytical result of $\beta =36\mu $, shown as a dashed brown curve, and the values of $\left(\mu ,\beta \right)$, shown as green points, obtained from (14).

**Figure 12.**The (

**left panel**) shows the mode shift of ${p}_{n}$ in (14) from $n=6$ to $n=5$ as ${p}_{6}$ decreases from $0.27$ to $0.25$. In the (

**right panel**), the red points depict $\left({p}_{5},{\mu}_{2}\right)$ obtained from ${p}_{n}$ and subjected to the constraint $\u2329n\u232a=6$, and the Gaussian is shown as a dashed blue curve.

**Figure 13.**(

**Left panel**) shows that as ${p}_{6}$ decreases, the peak of ${p}_{n}$ shifts from $n=5$ to $n=4$, and eventually, ${p}_{n}$ becomes a monotonically decreasing distribution. The (

**right panel**) depicts a change in the shape of ${p}_{n}$ from a monotonically decreasing to a U-shaped distribution for small values of ${p}_{6}$. In both panels, it is assumed that $\u2329n\u232a=6$.

**Figure 14.**Four artificially generated networks, by random fragmentation (

**top-left**and

**top-right panels**), Feynman diagrams (

**bottom-left panel**), and the Poisson network (

**bottom-right panel**), are compared to the probability distribution ${p}_{n}$ in (14) with the constraint $\u2329n\u232a=6$. The blue curves in ${P}_{\mathrm{Fragmentation},\phantom{\rule{4pt}{0ex}}c}\left(n\right)$, ${P}_{\mathrm{Fragmentation},\phantom{\rule{4pt}{0ex}}e}\left(n\right)$, ${P}_{\mathrm{Feynman}}\left(n\right)$, and ${P}_{\mathrm{Poisson}}\left(n\right)$ correspond to (20), (21), (22), and (23), respectively.

**Figure 15.**The (

**left panel**) shows truncated hexagonal tiling, with ≈66% triangles and ≈34% dodecagons. The (

**right panel**) shows ${p}_{n}$ in (14) as ${p}_{6}\to 0$ and $\u2329n\u232a=6$.

**Figure 16.**In the top row, we have shown Voronoi tessellations of the three cone photoreceptor subtypes, (blue) short-, (green) medium-, and (red) long-wavelength-sensitive cones, in a living human retina in Figure 1. The fraction of n-sided bounded polygons, ${p}_{n}^{\mathrm{color}}$, in each case reads ${p}_{4}^{b}=0.286$, ${p}_{5}^{b}=0.286$, ${p}_{6}^{b}=0.143$, ${p}_{7}^{b}=0.214$, and ${p}_{8}^{b}=0.071$; ${p}_{3}^{g}=0.010$, ${p}_{4}^{g}=0.089$, ${p}_{5}^{g}=0.300$, ${p}_{6}^{g}=0.360$, ${p}_{7}^{g}=0.153$, ${p}_{8}^{g}=0.069$, and ${p}_{9}^{g}=0.020$; ${p}_{4}^{r}=0.077$, ${p}_{5}^{r}=0.300$, ${p}_{6}^{r}=0.378$, ${p}_{7}^{r}=0.184$, ${p}_{8}^{r}=0.030$, and ${p}_{9}^{r}=0.030$. The Voronoi tessellation of the whole retinal field is illustrated at the bottom, with the fractions of n-sided polygons as ${p}_{4}=0.012$, ${p}_{5}=0.171$, ${p}_{6}=0.718$, ${p}_{7}=0.086$, and ${p}_{8}=0.012$.

**Figure 17.**Blue, green, red, and black points depict the experimental values of $({p}_{n}^{b,g,r},{\mu}_{2})$, $n=5,6$, for human cone mosaics (the black point represents the whole pattern of cones). Lemaître’s law is shown as dashed gray curves.

**Figure 18.**The (

**left panel**), adapted from [58], shows the spatial distributions of cone photoreceptors in the retina of a living human eye at a range of retinal eccentricities. In the (

**right panel**), we have depicted the cones’ behavior—the whole pattern in each case—concerning Lemaître’s law.

**Figure 19.**Voronoi tessellations of the spatial arrangements of the rodent cone subtypes and its whole retinal field (Figure 5) and the corresponding cones’ behavior concerning Lemaître’s law. Violet and green colors represent the short- and long-wavelength-sensitive cones, respectively. The points in the plots correspond to the experimental values of $({p}_{5,6}^{v,g},{\mu}_{2})$. The black point corresponds to the whole retinal mosaic. Lemaître’s law is shown as dashed gray curves.

**Figure 20.**Voronoi tessellations of the spatial arrangements of the dog cone subtypes and its whole retinal field (Figure 6) and the corresponding cones’ behavior concerning Lemaître’s law (dashed gray curves). Green and red colors represent the short- and long-/medium-wavelength-sensitive cones, respectively. The points in the plot correspond to the experimental values of $({p}_{6}^{g,r},{\mu}_{2})$, and the black point represents the whole retinal mosaic.

**Figure 21.**Voronoi tessellations of the spatial arrangements of the monkey cone subtypes and its whole retinal field (Figure 7) and the corresponding cones’ behavior concerning Lemaître’s law (dashed gray curves). Blue, green, and red colors represent the short-, medium-, and long-wavelength-sensitive cones, respectively. Experimental values of $({p}_{5,6}^{b,g,r},{\mu}_{2})$ are shown as points in the plots. The black point represents the whole retinal field.

**Figure 22.**Voronoi tessellations of the spatial arrangements of the human cone subtypes and their whole retinal field (Figure 8) and the corresponding cones’ behavior concerning Lemaître’s law. Short-, medium-, and long-wavelength-sensitive cones are represented by blue, green, and red colors, respectively. Lemaître’s law is shown as dashed gray curves in the plot and experimental values of $({p}_{6}^{b,g,r},{\mu}_{2})$ as points with their respective colors. The black point represents the whole retinal field.

**Figure 23.**Voronoi tessellations of the spatial arrangements of the zebrafish cone subtypes and its whole retinal field (Figure 9) and the corresponding cones’ behavior concerning Lemaître’s law (dashed gray curves). Blue-, UV-, red-, and green-sensitive cones are shown with their respective colors. Experimental values of $({p}_{6}^{b,\mathrm{UV},r,g},{\mu}_{2})$ are depicted as points in the plot. The black point corresponds to the whole retinal field.

**Figure 24.**Voronoi tessellations of the spatial arrangements of the chicken cone subtypes and its whole retinal field (Figure 10) and the corresponding cones’ behavior concerning Lemaître’s law. Violet, blue, red, and green colors represent their respective wavelength-sensitive cones. White color corresponds to double cones. Lemaître’s law is shown as dashed gray curves in the plot and experimental values of $({p}_{6}^{v,b,r,g,d},{\mu}_{2})$ as points with their respective colors. The black point corresponds to the whole retinal field.

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**MDPI and ACS Style**

Beygi, A.
Universality of Form: The Case of Retinal Cone Photoreceptor Mosaics. *Entropy* **2023**, *25*, 766.
https://doi.org/10.3390/e25050766

**AMA Style**

Beygi A.
Universality of Form: The Case of Retinal Cone Photoreceptor Mosaics. *Entropy*. 2023; 25(5):766.
https://doi.org/10.3390/e25050766

**Chicago/Turabian Style**

Beygi, Alireza.
2023. "Universality of Form: The Case of Retinal Cone Photoreceptor Mosaics" *Entropy* 25, no. 5: 766.
https://doi.org/10.3390/e25050766