Hyperuniformity — A Hidden Order Found in the Greatest Set of Eyes

Of all the things evolution has stumbled across, the eye is one of the most remarkable. Acting as sort of a ‘biological electromagnetic transducer’, the eye converts incoming photons into electrical and chemical spikes, known as action potentials. These spikes then drive the brain of the host life form. Billions of years of natural selection has produced several types of eyes, with some better than others. It would be an honest mistake to think that the human eye is at the top of the food chain, as this is not the case. Mammals underwent a long stint scurrying around in dark caves and crevasses, causing our eyes to take a back seat to other more important functions, such as the development of a cortex.

There are color sensitive cones in all eyes. Mammals have three types of cones, which are…wait for it…Red, Blue and Green. Our red and green cones are relatively recent on the evolutionary timescale – appearing about 30 million years ago.

The way these cones are distributed around our eyes is not perfect. They’re scattered around in lumpy, uneven patterns, and thus give us an uneven light sampling of our world. Evolution simply has not had enough time to optimize our eyes.

There is another animal on this planet, however, that never went through “the dark ages” as mammals did. This animal has been soaring high above its predators for over 60 million years, allowing its eyes to reach the pinnacle of the natural selection process. A bald eagle can spot a mouse from over a mile away. Birds eyes have 5 types of light sensitive cones – red, blue and green like our own. But add in violet and a type of cone that can detect no light, or black. But it is the way these cones are distributed around the bird’s eye that is most fascinating, and the subject of today’s article.

A Hidden Order

[Joe Corbo] of Washington University in St. Louis was studying the eye of a common chicken, when he came across a most interesting find. The way the light cones were distributed was unlike anything that he’d seen before. These light cones are random in human eyes and laid out in neat columns and rows in fish eyes. But there was some type of unique structure going on with the light cone distribution in the chicken’s eye.  The five types of cones themselves were laid out in a random pattern, but the same types of cones were never found close to one another. Imagine taking a handful of marbles composed of five different colors and tossing them on the floor, and finding an equidistant spacing between each of the colors.

There was clearly some type of hidden order within the seemingly random distribution of the light cones. [Corbo] wondered why they were not distributed in a grid or lattice type of structure, as that would seem to be the most efficient way to sample light from the outside world. Why did evolution opt for this pattern? It quickly became clear to [Corbo] and his colleagues that they were missing something… there was some type of variable at work that they did not understand.


Spheres optimally packed via Wikipedia

After some research, [Corbo] sought the help of [Salvatore Torquato], a  professor at Princeton and a recognized expert in packing — the study of fitting the largest of amount of objects in a set of constraints. [Corbo] wanted to know if the light cones in the chicken’s retina were optimally ‘packed’. A few images and algorithms later, it was found that they were indeed packed with optimum efficiency.

What was most surprising to [Torquato], however, was that packing was a physical manifestation, which has been seen in everything from crystals to large scale structures in the universe. And here it was again staring back at him… through the eye of a common chicken.


There is a particular pattern that forms when objects are optimally packed. It was this pattern that [Corbo] recognized in the chicken’s eye. It’s been dubbed “hyperuniformity”. What makes the chicken’s eye unique is that the light cones are all different sizes. Consider the following demonstration:

Lay out a bunch of pennies on a table, and then pack them to their most dense state. You will get a nice regular repeating triangular lattice type of pattern. If you toss in a few other sized coins, this pattern gets disrupted. Now imagine having five different sized coins optimally packed.  There is no longer any type of pattern… geometry forces this to be true. And this is why the five light cones are distributed without any type of pattern in the chicken’s eye. But, and this is a big but, evolution will demand an even distribution of the different types of light cones, and this gives rise to the hyperuniformity in the chicken’s retina.

Source via Lucy Reading-Ikkanda

Let us tickle your brain a little more by looking at hyperunifority from a semi-mathematical perspective. Imagine a lattice of pegs and some rings. We toss the rings onto the lattice and count the number of pegs within the ring. This number will vary slightly as the number of pegs along the edge of the ring will be different for each toss. We can observe that as the ring grows in size, this variance increases. So that for small rings, the number of pegs within the ring is always the same. But for larger rings, the number of pegs covered becomes slightly different. We find that the number of pegs covered is proportional to the ring’s perimeter for both large and small rings. See the image to the left.

Now imagine that our pegs are laid out in a completely random pattern. In this case, we will find variance in the number of pegs contained within both small and large rings. The variance will be much greater than the lattice pattern, especially with the large rings. We find that the number of pegs covered is proportional to the ring’s area for both large and small rings.

Something strange happens if we have a hyperuniform pattern. Let’s make the pegs random, but equidistant from each other… like the light cones in a bird’s eye. We find that the number of pegs within the small rings will vary in a similar way that they do with the random peg layout — by area. But not so for the large rings. With those, we find that the variation is similar to the lattice layout — by perimeter. This suggests that even though the pattern is random, the large scale density is the same as the non-random lattice layout.

There is much more to be said on hyperuniformity and Quanta Magazine has a great article that delves a bit deeper. Nature has a knack for pulling off some amazing tricks and they’re often found in very common places.

62 thoughts on “Hyperuniformity — A Hidden Order Found in the Greatest Set of Eyes

  1. I never thought of the eye as all that amazing; very limited light spectrum range, very limited focal range and very limited intensity range. They are also not very durable and very fragile. Excuse me while I go clean my glasses.

    1. Limited spectrum range -> but the spectrum range happens to be at least reasonably useful in daily life
      Limited focal range -> well, we don’t have zoom, but focal distance is infinity to a few inches in the ideal no-glasses-required case
      And limited intensity range??? This is where eyes shine. The same eyes can see a bright outdoor scene, or stars. Compared to any common image sensing technology, digital or film, eyes still have a higher dynamic range. Some black and white slide film approaches that of eyes, and modern high dynamic range signal processing technologies can approach that, usually with multiple stacked exposures. But, sit in a dark-ish room with an open window on a bright day. Look around, note how you can see both inside and outside *at the same time.* Now, try the same with a digital camera — good luck getting a single image where nothing’s over or underexposed!

      1. Lister: Any problems?
        Kryten: Well, just one or two. In fact I’ve compiled a little list if you’ll indulge me. Now then, uh, my optical system doesn’t appear to have a zoom function.
        Lister: No, human eyes don’t have a zoom.
        Kryten: Well then, how do you bring a small object into sharp focus?
        Lister: Well, you just move your head closer to the object.
        Kryten: I see. Move your head … closer, hmm, to the object. All right, okay. Well, what about other optical effects, like split screen, slow motion?
        Lister: No. We don’t have them.
        Kryten: You don’t have them – just the zoom? Hmm. Well, no, that’s fine, that’s great, no, no, that’s really great, that’s great.

    2. That’s because we mammals have the “undergrad freshman God’s first eyeball project” model of eye. Honestly, there are so many things wrong with the design that it’s a marvel we can see at all.

      1. This common misconception is due to our lack of understanding, rather than deficiency in “the design”. Given that it self evidently [and unarguably] works very well at the system level, it would be a better use of our time to first think “I don’t have the full picture” and so ask “why is it done this way?”, than naively assume we have enough knowledge to say “it doesn’t look like how I’d have done it”.

    3. as someone else has said, the eye is a mediocre or even bad photography equipment, but have you ever tried to make a lens out of jelly? With that into consideration, the eye is excellent equipment.

      1. A mediocre* sensor backed by sophisticated signal processing. Luminance, chroma, edge detection, focus, movement detection, distance, interpolation, and more – co-ordination with other senses, for example. Ever watched a video and detected a mis-match between the audio and the actor’s lip movements? That can be as little as three frames (~1/8 second). And no, I don’t mean watching dubbed episodes of Samurai or Monkey Magic :-)

        * it’s self-healing for minor injury. Scratch a camera lens, throw it away. It’s also self-cleaning. It can even heal from moderate injury. OTOH it deteriorates with age and UV exposure.

  2. NO! NO! NO! In a random distribution the VARIATION of the number of dots inside is (usually) the square root of the number of points inside. Since these is proportional to the area, the variation is proportional to the square root of the area, i.e., to the perimeter. The picture is so wrong that it is not even funny.

    1. If we’re going to nitpick. IIRC we humans have something like “intensity” sensors, and two types “difference-between-two-colors” sensors. From the three numbers you can reconstruct all the red-green-blue that you might want. Just like a digital camera reconstructs each pixel value from an RGGB matrix, or for different brands a matrix with differnt colors (CYM IIRC, but I don’t know which one, if any, wwas doubled like the green in the RGB matrix).

  3. > Evolution simply has not had enough time to optimize our eyes.
    It had plenty of time, don’t expect them to improve in the future. I’d rather think that the reason that the eyes aren’t any better is that there a diminishing returns and they’re good enough for their purpose. Other factors become much more important for success as a species.

    Now, why did we develop self awareness …

      1. There is apparently a retinal pre-processor. There is not enough bandwidth for the visual cortex to get all the information required from simple photoreceptors. Lots of vertical, horizontal, edge, and motion detection. The visual cortext makes up a story that matches the compressed data from the retina.

  4. I have to chuckle when I read comments about how fragile or inferior humans are when compared to other technology. As far as I can tell humans are the most eloquent piece of engineering in existence.

    Currently there are around 7 billion of us. We are completely self-contained, self-healing, and with an opposite gendered human self-reproductive. We are creative and highly adaptable. In extremely harsh environments our creativity compensates for physical inadequacies. There is no other machine in existence that can process the range of “shit” we can and still remain functional. So called AI/robotics can’t even come close to our energy density and adaptability. Most of us well exceed the warranty period of any product in production today, especially given our complexity.

    Here is the Turing test for Ai/Life. When you can do this with a robot you may convince me that you are on to something.

    Take a Navy Seal. Equip them with a pocket knife and a box of Twinkies. Blind fold and fly him to a remote part of the world. I would expect that within 24 hours he would have found a water source, food source, and established his location. In addition he would have a plan on how to escape his situation back to civilization.

    Match that!

  5. Nice article as a very first start into the topic. However, I really disliked a few things:

    “These spikes then drive the brain of the host life form.”

    No, they don’t. No nerve signals from any sensor “drive” the host life form’s brain, according to current brain sciences.

    “There are color sensitive cones in all eyes.”

    No, there aren’t. There are LIGHT sensitive cones in all eyes, but not all eyes are color sensitive.

    “Evolution simply has not had enough time to optimize our eyes.”

    No, it had. It just wasn’t necessary. In fact, OUR eyes ran into a dead end anyway, because their sensors are facing BACKWARDS. If we were constructed by some kind of God, we really should file a complaint, because no God would be dumb enough to construct eyes backwards (then again, there’s reason to believe that Gods can be a tad dumb at times).
    (To be fair, there are actually theories about why that backwards-construction may have made sense at some point in time, which has to do with too light sensitive models for the sensors …)

    “Why did evolution opt for this pattern?”

    It didn’t. Evolution does not “opt” for anything, evolution is not a conscious entity that “opts”.

    What I am nitpickiing at is, while the article as such is really well intended, it is this “let’s pretend evolution makes sense” or “is conscious”, that makes understanding evolution so hard for many people (not just around the biological topic). Not “humanifying evolution”, which sometimes just sounds as if “evolution” is a layman’s term for “God”, would help the cause: Evolution is a process that more often than not generates failures. It is the quantity of variations over the quantity of time that makes evolution seem “successful”, in the long run it may be. But is doesn’t opt, it never “optimizes” and it does not calculate.

    1. “n fact, OUR eyes ran into a dead end anyway, because their sensors are facing BACKWARDS. If we were constructed by some kind of God, we really should file a complaint, because no God would be dumb enough to construct eyes backwards (then again, there’s reason to believe that Gods can be a tad dumb at times).”

      Let’s not make rash statements as there are other good reasons why the sensors need to be where they are.


      Statements that claim that “god wouldn’t have done it like that” are often made to jump to conclusions before a complete understanding of a “design” is achieved.

      Design/evolution is a compromise and it’s important to look at the advantages/disadvantages of the compromises.

  6. Although well intended, this is not how evolution works. Too many people think evolution decides what to do or through time makes things optimum Evolution, like design, ends up with compromises.

  7. OK Ill just leave this here. Intelligent Design. BOOM!
    So my reading of the irreducible complexity argument on wiki falls over where it states a complex system will not work as efficiently without a key part. In a lot of cases the system will not work AT ALL. Ie glucose transport proteins on placental villi. Without these very specific and complex molecules which had to ‘evolve’ all at once, mammalian life would simply not exist, no?

    1. Matt, the part you are missing is that the way things are aren’t they way they have always been. The physical analogy is that of a self-supporting arch made of stones. If you remove any one stone, the arch collapses. But when it was being built, there was a support structure beneath the arch which allowed the arch to be built before the support structure was removed.

      Creationists will retort: but, but someone designed the arch! Checkmate! Well, duh, it is an analogy that is designed to convey one specific idea, not that the two systems are identical. The same thing happens in natural arches where erosion undercuts some rock leaving a natural arch above it. That type of arch can form by happenstance without any guided intelligence.

      Getting back to irreducible complexity, Behe (the guy who coined the term) has never defined what irreducible complexity is — it is an ill specified idea that can’t be measured, but creationists know it when they see it.

      If a theory of evolution requires a bunch of parts to evolve at once, then that theory is broken. Is is creationists who claim that complex biological systems appeared at once, not biologists.

    2. *None* of the molecules in any life form evolved all at once. This is a clear misunderstanding of what evolution fundamentally is. Life “evolved” one chemical at a time. Perhaps before arguing about how something is false you should try to understand what it is. The “It’s complicated, therefore it can never be understood” argument need to die. No one person will understand everything, but one person can understand anything.

      1. One nitpick. One person cannot undestand anything. Example from a famous physicist: chimps cannot comprehend calculus. Its been proven that they lack the brain capabilities to understand the base concepts. We have not uncovered all the concepts at work in the universe, so there is no guarantee that we can understand everything.

  8. Here is something to think about, my children have far better eyes than I do, but I can see better than they can.

    Oh and that cell distribution thing, well it is obvious when you know how gene expression influences cell differentiation and tissue formation. It has a lot to do with chemical signal gradients, which can act like a combination of pushing and pulling between participating cells, this leads to the distribution type seen in eyes and if that in any way boosts the fecundity of the organism that gene configuration will propagate through the population. The end result may look complicated but the processes involved are elegantly simple.

  9. our eyes see in Red.Green.Blue. ???

    more like Red.Yellow.Blue. when you look at a graph on a linear scale.

    if you draw a LOGICAL rainbow over the nano-meter scale, there is a serious mixup with our h***-sapien cone cells, with the execption of a small tribe in a small region on earth.

    this group possess PROPER color vision where “green” cones are centered between red and blue, i forget the tribe/area where these people live but its so impoverished that we have yet to study the cone cells of them. (due to strict burial rituals ect). thier system of language used to describe colors is incompatible with ours, with several shades of (simillar looking) green being labeled as different colors. unfortunately they have difficulty telling red and orange apart, just like many people on this planet have difficulty telling “pure-green” and aqua apart (or aqua vs cayan or cayan vs royal-blue)

    PS: our brightness nightvision cones (aka luminance) bridges the gap between green and blue… swhy we often confuse grey with cayan in low-light conditions and red doesnt disturb nightvision… because nightvision does not detect red at all.

    PPS: no word on if these people are _ACTUALLY_ sapien like the rest of us, or gene-mixes from before us h***-sapiens completely wiped all the other h***-species off of this planet, i have no idea if anyone has tested thier DNA yet.

    1. You do realize that you don’t have to censor anything, right? Maybe it was a joke, whatever…

      That tribe sounds interesting. It might be a nutritional difference causing the altered vision, but that’s just my medically-uneducated speculation.

      I found some info!
      The Himba tribe from northern Namibia.

      Color/colour vision is such a subjective perception; I wonder if my ‘blue’ is the same as anyone else’s. ;)

      1. That’s an old philosophical question, but I think the answer is almost certainly yes. You’ve got the same hardware as everyone else. We know now what perception is, how it works, at least more than the ancients who asked that question.

      2. Even if that study wasn’t iffy, it’s still more akin to the fact that Australians call yellow lights orange lights, and Japanese people call green lights blue lights. It’s all a matter of the arbitrary subdivisions of the visible spectrum which might vary between cultures.

  10. > Mammals have three types of cones
    Most mammals have only two types. As far as I know, only some primates have the third type. So, we are actually very lucky with our eyes.

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