
Hyperuniformity Found In Birds, Math And Physics - clumsysmurf
https://www.quantamagazine.org/20160712-hyperuniformity-found-in-birds-math-and-physics/
======
gregschlom
A beautiful article from Mike Bostock that illustrates this (and other)
principles:
[https://bost.ocks.org/mike/algorithms/](https://bost.ocks.org/mike/algorithms/)

And my attempt at using Poisson-disc sampling to generate stippling patterns
in real time in a GPU shader:
[http://gregschlom.com/devlog/2015/01/31/stippling-effect-
scr...](http://gregschlom.com/devlog/2015/01/31/stippling-effect-
screenshots.html)

I wish my blog post had more details on the technique, but basically I am pre-
computing Poisson-disc distributions at several (255) density levels in such a
way that the samples are adaptive (ie: all samples from levels 1-n are also
samples at the level n+1.

I'm then storing that information in a texture, and reading from it in a
shader to know whether or not to draw a stipple.

The tricky part is to figure out how to do that on arbitrary 3D surfaces.

~~~
kordless
Mike's stuff is awesome. I just watched the animation of one of the optimum
solutions and I realized that all the placements are interdependent on each
other. It's a holistic approach, instead of an algorithmic approach.

------
twic
A while ago (file timestamps say 2005), a colleague of mine was studying CCR5,
a cell surface receptor which HIV exploits to enter cells. She had taken
electron microscope pictures of the distribution of CCR5 over the surface of a
cell. By eye, it was clear that it was distributed evenly, but it was
suspiciously even - not random, but well spread out, exactly as in these
hyperuniform cases.

I wrote some Python scripts to calculate Ripley's K-function, which looked
like a good way of quantifying this:

[http://www.thorsten-wiegand.de/towi_methods.html](http://www.thorsten-
wiegand.de/towi_methods.html)

But she didn't think the distribution was as interesting as i did, and never
used them!

~~~
untilHellbanned
As a biologist, I'm not surprised. I'm sure there was something quite
meaningful happening but most biologists lack the fortitude to venture into
unknown areas or new disciplines. Its a highly risk-averse crowd.

~~~
77pt77
Doubt that was the reason.

I'd bet math phobia.

People working in Biology usually are not Math savy and are proud of it. Many
of them are there to run away from other scientific Math intensive fields.

Anyone suggesting anything along this lines will be immediately shut down just
because of that.

~~~
twic
I think it was just that she didn't see it as relevant to the problem she was
trying to solve at the time.

------
Phemist
Amazing! This seems very similar to something I was taught about during my
post-grad (and regret not pursuing, if only for this cool effect -
[https://en.m.wikipedia.org/wiki/Pinocchio_illusion](https://en.m.wikipedia.org/wiki/Pinocchio_illusion)).
These were cortical maps ir cortical receptive fields in lower level sensory
cortex of animals, for example barrel cortex of rats that processes whisker
input. Areas that were sensitive to different deflection angles seemed to
self-organize like this, with seemingly random organization looking at high
frequency features, but becoming more ordered at lower frequency features.
Specifically, "pinwheels" seemed to form, areas where all different deflection
angles were represented in the map, and all these areas touched into a single
vanishing point.

Like in the article the paper referenced below openly speculates about the use
of organizational structures like this.

Edit: Sorry, this was written from my phone.

Relevant paper:
[http://onlinelibrary.wiley.com/doi/10.1002/dneu.22281/abstra...](http://onlinelibrary.wiley.com/doi/10.1002/dneu.22281/abstract)
(use scihub)

------
lcrs
Strikingly similar to the low-discrepancy sequences used as sampling patterns
in modern ray tracers - and quite a similar role, really:

[https://en.wikipedia.org/wiki/Halton_sequence](https://en.wikipedia.org/wiki/Halton_sequence)

[https://books.google.co.uk/books?id=DirOQ_PELlgC&lpg=PA999&o...](https://books.google.co.uk/books?id=DirOQ_PELlgC&lpg=PA999&ots=XqES6WpvhI&dq=pbrt%20halton&pg=PA321#v=onepage&q=halton&f=false)

~~~
jacobolus
I don’t think low-discrepancy sequences have quite the same kind of structure
as these “hyperuniform” distributions. There don’t seem to be any papers which
explicitly compare them though,
[https://scholar.google.com/scholar?q=hyperuniformity+halton](https://scholar.google.com/scholar?q=hyperuniformity+halton)

~~~
jxy
I think some of the sequences are similar. The particular wikipedia entry of
Low-discrepancy sequence [0] mentions Poisson disc.

[0] [https://en.wikipedia.org/wiki/Low-
discrepancy_sequence](https://en.wikipedia.org/wiki/Low-discrepancy_sequence)

------
dharma1
Fascinating. Two main things that stood out for me

1) Hyperuniform materials can be transparent - and have direction independent
band gaps -
[http://arxiv.org/pdf/1510.05807v3.pdf](http://arxiv.org/pdf/1510.05807v3.pdf)

2) You can induce irreversible hyperuniformity in some emulsions by shaking
them at certain amplitude -
[http://arxiv.org/abs/1504.04638](http://arxiv.org/abs/1504.04638)

Surely there is an opportunity for some DIY garage physics here :)

------
Vexs
You can see a pretty concrete example of this in forests, the trees are all
densely packed, and random- and thus fall under hyperuniform. (as far as I can
tell, anyway. Haven't exactly tested it, but it sure looks hyperuniform.) I've
noticed it in a handful of other things, but I never knew there was an actual
thing behind it.

Absolutely fascinating, and it's applications in materials are amazing.
Whatever-direction bandpass filters? Crazy cool.

~~~
azeirah
I remember seeing a documentary were some scientist's work on forest/tree
distribution was shown.

In the forest they measured, the fractal shape of the tree actually extended
to the forest itself, as if the forest itself is one big "tree" with actual
trees as its branches.

(Though, trees are 3D fractals, forest is a 2D plane, how does that work?..)

~~~
Vexs
It probably has to do with seed dropping patterns, and where light is.
Fascinating stuff though.

------
im3w1l
Having regularly spaced sampling causes aliasing, where frequencies above the
nyquist limit will look like lower frequences. Irregular spacing can, under
some assumptions about the signal, avoid this. This an be used for super
resolution.

~~~
colanderman
Was wondering exactly this. I wonder if avian vision benefits from the greater
frequency resolution this pattern provides.

------
joshu
Reaction-diffusion could easily generate these patterns. There are several
places in parameter space that look possibly correct.
[http://mrob.com/pub/comp/xmorphia/index.html](http://mrob.com/pub/comp/xmorphia/index.html)

------
pfd1986
Also similar to what is done in stippling art:
[http://blog.wolfram.com/2016/05/06/computational-
stippling-c...](http://blog.wolfram.com/2016/05/06/computational-stippling-
can-machines-do-as-well-as-humans/)

------
jpfed
It looks like Poisson disk noise.

~~~
pablobaz
Yes I thought the same. See: [http://devmag.org.za/2009/05/03/poisson-disk-
sampling/](http://devmag.org.za/2009/05/03/poisson-disk-sampling/)

and for a D3 animated example:
[https://bl.ocks.org/mbostock/dbb02448b0f93e4c82c3](https://bl.ocks.org/mbostock/dbb02448b0f93e4c82c3)

------
aznpwnzor
Makes a lot of sense that uniformity with constraints is exactly what nature
likes, wonder if hyperpossoinity is exploited by nature or more likely can be
exploited by human designed systems.

------
andrewflnr
So this is a better name for what they were calling "universality", right?

... Stuff like this makes me want to throw everything away and study math
fulltime. That's still an option if I ever get FU money. Be sure to click
through to the related article about the (spoiler) meteorite fragment
containing a quasicrystal.

------
carlob
I find it funny that Joe Corbo didn't start from ravens. Am I right? :)

------
jsnsjsfnts
This is just an occurrence of the principle of least action. Systems
exhibiting "hyperuniformity" just arrange themselves in order to minimize
their potential. This is pretty standard stuff in engineering, and is the
basis for finite element simulations of structural mechanics and fluid
dynamics problems.

~~~
pfd1986
That is not strictly true. Most systems "minimizing their potential" exhibit a
crystalline, ordered arrangement. Hyperuniform patterns are definitely a
result of an optimization, but in this case it is a more complicated one than
a 'potential energy'.

~~~
trhway
>Most systems "minimizing their potential" exhibit a crystalline, ordered
arrangement.

crystalline structures have lower entropy compensated by increase in the
entropy of the environment due to heat being transferred out of crystalline
structure during its formation.

It is kind of intuitively obvious that hyperuniform(random) forest have higher
entropy than crystalline style ordered forest would have. I don't see
connection to environment (like heat transfer in crystal case) that would
allow to compensate for decrease of entropy in an ordered forest.

~~~
pfd1986
That is a good point. But without getting too technical (although I'd love too
if wanted), there are 2 caveats with your thought: 1\. Order does not need
heat transfer. Flying birds form a V-shaped pattern (to minimize drag,
whatever), fish "order" into a packed school instead of being random, a
honeycomb is hexagonal. Those are (near) optional solutions for constraints.
There is an analogy with crystal formation but the math is not totally clear.
2\. Crystals can have higher entropy than disordered states. Actually, a
(crystalline) dense packing of Brownian spheres have higher entropy than a
random close packing of spheres.

~~~
goodmachine
Interesting. Please feel free to get more technical.

~~~
pfd1986
About the 2nd point there is this video you can watch which might do better
than anything I can type:
[https://www.youtube.com/watch?v=chS8dpGB0E0](https://www.youtube.com/watch?v=chS8dpGB0E0)

~~~
goodmachine
Thanks!

