
Why nature prefers hexagons - bsg75
http://nautil.us/issue/35/Boundaries/why-nature-prefers-hexagons
======
Pulcinella
You get hexagons because of close-packing.[1] Circles (or a 2D array of
spheres) of the same size fit closest together when they are arranged in a
hexagonal pattern. Push a bunch of marbles together and that's what you get.

The bees don't know anything about hexagons. They just make circles close
together and then as the cells are filled, stepped on, and come into contact
with other wax cells, they "ballon out" into a hexagon shape.

[1][https://en.m.wikipedia.org/wiki/Close-
packing_of_equal_spher...](https://en.m.wikipedia.org/wiki/Close-
packing_of_equal_spheres)

~~~
stinos
Is this the generally accepted explanation now? (I thought so, but the article
itself doesn't mention it - then again, the article seems full of pseudo-
science)

~~~
cygx
Not sure if bees might do it this way - but just looking at pictures of early
stages of nests such as [1] or [2], wasps apparently don't: It looks as if
they do construct proper hexagons from the get-go.

[1] [http://www.localhoney.co.uk/wp-
content/uploads/2010/06/start...](http://www.localhoney.co.uk/wp-
content/uploads/2010/06/start-of-small-wasp-nest.jpg)

[2]
[http://1.bp.blogspot.com/-uM7ATVMEcDA/TdcWZm9BPEI/AAAAAAAAI8...](http://1.bp.blogspot.com/-uM7ATVMEcDA/TdcWZm9BPEI/AAAAAAAAI8w/9q7bDCoP34E/s1600/2.jpg)

~~~
stinos
Good find, that definitely looks hexagonal from the start.

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ineedasername
I really dislike when articles use words such as "prefer" in this way. It
conveys a level of intentionality that is not truly present. It would be
better to say "Why hexagons appear often in nature." Or "Why nature produces
hexagons"

Otherwise, the descriptor is not just imprecise, it is also misleading.

~~~
thaumasiotes
You may have a more spiritualistic view of "intentionality" than is really
warranted.

~~~
freshhawk
Or they, like me, have constant interactions with lay people who constantly
understand these things to mean their view of a universe guided by an
intelligence is correct.

I get it, it's just hard to avoid in English, but it is still a (small)
failure in clear science communication.

~~~
saghm
I think the worst case of this in science is the way that evolution is
described in a way that implies an active process rather than just random
mutations which may or may not make organisms more fit for survival.

~~~
freshhawk
Yeah, I think that's the most common one. Strongly connected with the idea
that evolution is "improvement" or some kind of step along a road to being
"better", which I've seen trip up a lot of people who normally don't get
confused about this kind of thing.

~~~
TheSpiceIsLife
This reminds me of a thing a comedian said, or at least that's where I heard
it first.

"also told you we're descended from apes ... you lot might be, I'm ascended
from the apes" \- Steve Hughes[1]

1\.
[https://www.youtube.com/watch?v=CYk5k-vL_Ek#t=1m50s](https://www.youtube.com/watch?v=CYk5k-vL_Ek#t=1m50s)
\-- caution, course language

------
jacobr
Started working on a game with hexagons a while back, and there are really
weird/cool things related to hexagons online.

Global Hexagonal Awareness Resource Center:
[https://hexnet.org](https://hexnet.org)

> It is likely that HEXAGONS will continue to increase in popularity over the
> coming years, as humanity enters a glorious new hexagonal golden age, and
> all sentient beings on our planet ascend to a new, higher state of hexagonal
> consciousness.

[http://hexagons.info](http://hexagons.info)

~~~
jacquesm
Interesting! My eldest has been working on sketches for a game he calls 'Hex'.

------
robbrown451
Always wished pixels were hexagonal. Yeah the math would be a bit harder and
vertical lines would be fuzzier at low resolution, but still....
[https://www.quora.com/Why-are-computer-pixels-
square](https://www.quora.com/Why-are-computer-pixels-square)

~~~
tzs
I wonder how hard hexagonal pixel layout would have been to do on a CRT?

Two ways come to mind. If the basic scan line is kept horizontal, then a small
vertical modulation on each scan line could result in a hexagonal layout if
you timed it right.

Alternatively, if the grid is tilted (so that the basic scan line is diagonal
instead of horizontal), then you just have to offset the odd scan lines by
half a pixel from the even scan lines.

I think we are just lucky that we ended up with rectangular screens. Imagine
if they had went with circular screens. The scan might then easily have been a
spiral starting in the center. That's fairly easy to do. It's just a matter of
driving the horizontal and vertical deflectors with sine waves with the right
phase difference, with a saw tooth amplitude.

From a television point of view, I don't think it really matters which of
these you use, as long as the cameras and the displays use the same scan
pattern.

From a computer point of view, though, it would have been a lot more painful
if CRTs used a spiral scan. For most graphics applications we'd still need to
manipulate rectangular areas, and that would be quite annoying in a coordinate
system based on a spiral scan.

~~~
lightedman
Well, the problem there is that CRTs used a triangular-patterned phosphor
screen, excepting Trinitrons which had their phosphors lined up in a row. How
would you handle the missing spot for a phosphor in a hexagonal arrangement? I
guess with current tech, we could make ultra-fine phosphor groups that we'd
not be able to see. an 8K CRT at 32" would be quite nice .

~~~
Stratoscope
There was no correlation between the phosphor dots on a typical color CRT and
"pixels" as we think of them. It wasn't like the way we use an LCD or OLED
display at all. A color CRT had _no native resolution_ : display pixels were
not locked onto specific phosphor dots.

Consider all the analog adjustments a CRT offered: you could tweak the overall
height and width of the displayed image and nudge it up or down and left or
right. A high end CRT would have additional controls to adjust the _shape_ of
the image to correct for pincushion or barrel distortion. You could also drive
the CRT with different display resolutions. Obviously the phosphor dots didn't
move around when you did this.

Even on a Trinitron display there was no connection between logical pixels and
the aperture grill spacing.

A good analogy for today's displays would be an LCD/OLED display that you _can
't run in native resolution_, and can't even discover what its native
resolution might be: the pixels you generate in software are not directed to
specific physical points of light on the screen.

A monochrome CRT came much closer to having something that today we would
recognize as "pixels", because there was no shadow mask or phosphor dots.

Whatever problems might have stood in the way of using a hexagonal pixel
layout on a color CRT, the phosphor dot or stripe layout wasn't among them.

Edit/meta: I really wish people would not downvote comments like lightedman's
parent comment, which may have been wrong on the facts but provided an
opportunity for me to jump in with some hopefully interesting information that
not everyone may have known about CRT technology.

Some of the best conversations I've had have been where I've had a
misconception about something and someone was kind enough to set me straight
on it.

Yes, yes, I know, we're not supposed to complain about downvotes. So if my
complaint bothers you, here's my offer: downvote _this_ comment and upvote
lightedman's parent comment, which received some downvotes that I think were
undeserved. Fair deal?

~~~
lightedman
"A color CRT had no native resolution"

That is patently untrue, otherwise we'd have had 8K CRTs long ago. Maximum for
CRTs that I've ever had was 2048x1536.

"Obviously the phosphor dots didn't move around when you did this."

No but when you suddenly move to a hexagonal configuration, you've just
wrecked color gamut because you've now got groupings with a missing phosphor
(ideally in the center) adding a black tone overall.

I used to work as a TV repairman, and I've worked in TV manufacturing plants
as a design engineer. To address your next point "Whatever problems might have
stood in the way of using a hexagonal pixel layout on a color CRT, the
phosphor dot or stripe layout wasn't among them." That's how we discovered
30-ish years ago that a hexagonal layout was a BAD IDEA because it wrecked
color gamut AND increased X-ray radiation emitted because of lower rates of
absorption due to large holes in phosphor arrangements (that was back then,
again, nanotech now days might alleviate that using much smaler phosphors.)

"Even on a Trinitron display there was no connection between logical pixels
and the aperture grill spacing."

It was there for the purpose of beam convergence, which would make a 'sharp'
pixel or 'blurry' pixel no matter your chosen resolution. So yes, it's most
certainly connected.

"So if my complaint bothers you, here's my offer: downvote this comment and
upvote lightedman's parent comment, which received some downvotes that I think
were undeserved. Fair deal?"

No, let them downvote me. It adds to my friend's psychology paper on how
people are too lazy to speak up and instead talk with a simple mouse click
(Highlighted/targeted websites - Reddit, HackerNews, and Slashdot.)

~~~
Stratoscope
Thank you for the very interesting correction! It looks like I was the one who
was wrong on the facts... :-)

Just to clarify one point I made poorly, when I said color CRTs don't have a
native resolution, what I meant was that there was never an attempt to
precisely match up display pixels 1:1 with the phosphor dot grid or stripes.

Of course, if you tried to drive a CRT with a resolution that exceeded the dot
or stripe pitch, you wouldn't be happy with the results, so that did set a
practical upper limit on the resolution you could use, even if the electronics
otherwise could have supported a higher resolution.

------
simcop2387
PBS Infinite video on the same subject and how it expands into 4D space.
[https://www.youtube.com/watch?v=X8jOxEGVyPo](https://www.youtube.com/watch?v=X8jOxEGVyPo)

------
mcnamaratw
Strange article. You can see that some of the statements about honeycombs in
the first paragraph are wrong, just by looking at the first picture.

------
huac
Aren't triangles the strongest shape?

[https://math.stackexchange.com/questions/1393965/are-
triangl...](https://math.stackexchange.com/questions/1393965/are-triangles-
the-strongest-shape)
[https://www.reddit.com/r/askscience/comments/619ygo/why_are_...](https://www.reddit.com/r/askscience/comments/619ygo/why_are_triangles_the_strongest_shape/)

~~~
ecesena
I'm not sure. I think roofs are triangular mostly to make water/snow slide
down, while arcs are architecturally stronger, i.e. they can support more
weight.

So hexagons are better than triangles, and dodecahedron would be even better,
etc. but nature tends to simplicity.

------
gaius
Is this why France is hexagonal I wonder? Why aren't there more hexagonal
countries?

~~~
GuiA
France is only a hexagon if you squint really hard... its shape has also been
very arbitrary over the centuries

[https://upload.wikimedia.org/wikipedia/commons/a/ae/Frontier...](https://upload.wikimedia.org/wikipedia/commons/a/ae/Frontiere_francaise_985_1947_small.gif)

~~~
gaius
I think downvoters may be unaware of the history of the term:
[https://en.m.wiktionary.org/wiki/Hexagone](https://en.m.wiktionary.org/wiki/Hexagone)

------
ecesena
Or simply the product of the first two (prime) numbers is 6.

Similarly we have 10 fingers and we like base 10, but for time we prefer
something which is "better dividible" (pardon my english), i.e. 3x4x5 = 60.

------
tambourine_man
A bit too playful for me, but it gets the message across:

[https://youtube.com/watch?v=Pypd_yKGYpA](https://youtube.com/watch?v=Pypd_yKGYpA)

~~~
leke
And this, also from PBS
[https://www.youtube.com/watch?v=X8jOxEGVyPo](https://www.youtube.com/watch?v=X8jOxEGVyPo)

------
tyrw
I was really hoping the article would touch on Saturn's north pole hexagon, as
it completely blows my mind every time I think about it.

[https://en.m.wikipedia.org/wiki/Saturn%27s_hexagon](https://en.m.wikipedia.org/wiki/Saturn%27s_hexagon)

------
askvictor
Any relation to three-phase power being more efficient than single phase?

~~~
jacquesm
Three phase power is a way to evenly supply current to a motor while still
using AC.

It's not 'more efficient' as much as it is giving you a more even torque
because the current through the motor doesn't drop to 0 10's of times per
second, as it would with single phase. A nice side effect is that your motor
(or alternator) can be a lot smaller for the same amount of power, a single
phase motor would have to produce that power with the motor being at it's peak
only once per cycle rather than all the time.

------
pseudozach
how come buildings are made from rectangular bricks then? Would hexagons be
easier/more efficient to work with?

