Why nature prefers hexagons

http://nautil.us/issue/35/Boundaries/why-nature-prefers-hexagons

by bsg75 • 9 years ago

101 62 9 years ago

simcop2387• 9 years ago

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

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

tzs• 9 years ago

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.

robbrown4513• 9 years ago

Right. At least a hex grid is still essentially a 2-dimensional array. In most ways it would be identical to a rectangular grid, but the algorithm for sampling surrounding pixels would be slightly different because of the spacial arrangements.

lightedman2• 9 years ago

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 .

mjevans• 9 years ago

Analog circuits aren't my area of expertise. However it seems likely that the complexity of a stable and identical spiral scan circuit is either extremely difficult or possibly improbably expensive.

Compare the above to what we have in reality: it seems that there were some vacuum tube tricks that made a grid system much easier. https://en.wikipedia.org/wiki/NTSC#Technical_details

taeric• 9 years ago

There is a section in the manual for METAFONT that explains why a certain shaped pen is actually superior to a simple circle. I've always been curious if this was explored more for actual screen rastorization.

userbinator• 9 years ago

and vertical lines would be fuzzier at low resolution

Horizontal ones too.

Non-square pixels have been around for a long time in digital camera LCDs and more recently the https://en.wikipedia.org/wiki/PenTile_matrix_family but while they're fine for photos and other gradient-like images, text and lineart have a noticeable "grain" on them.

dogma1138• 9 years ago

Most lcd screens today use non-square pixels, OLED displays use non-equal sizes for different colors and o don't see anyone complaining about sharpness.

jacobolus2• 9 years ago

At this point, displays have fine enough resolution and GPUs are fast enough, that if you want to make hexagon-pixel images you can go right ahead and it won’t make too much difference (except you’ll reduce moiré artifacts), as long as you’re willing to implement your own code to rasterize the image to a square grid for display.

It would be neat if camera sensors and displays would switch to hexagonal grids of pixels – considering most images get resampled right before display now anyway, it should be all upside (except for a bit of extra implementation hassle).

A hexagonal grid is nice for several reasons: it can easily handle refinement to 3 or 4 subpixels per pixel, while a square grid needs 4 subpixels to keep its proper grid; it is much more isotropic than a square grid (straight lines at a variety of angles look much better); it is notably more efficient at covering the plane; hexagonal filters have a much nicer 2-dimensional frequency response; dithering works quite a bit better on a hexagonal grid; etc.

There are some printers that use a hexagonal grid, and some hexagon-pixel cameras used for stuff like medical imaging or astronomy.

ineedasername• 9 years ago

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• 9 years ago

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

freshhawk2• 9 years ago

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.

kirkules• 9 years ago

Rather, a large number of laypeople seem to have this more spiritualistic view, and it is fairly obvious how they will interpret this kind of language.

degenerate• 9 years ago

I agree, it makes the reader think the bee has some kind of foresight in the building process, like "hmm. here's my options, and I greatly prefer to build hexagons!"

It's not really their choice to prefer it. It's what works best and thus bees are programmed to do. Imagine an alien reading the headline "Why humans prefer sleeping prone"

labster• 9 years ago

I think I saw that article on a Minbari news site, right next to "The 11 Most Meditative Vacation Spots in the Earth Alliance".

vacri• 9 years ago

Hexagons are what you get when you squish a lot of semi-rigid round things together. It's not like the bees are designing hexagons - look at the cells on the free edges of a comb and you'll see little in the way of sharp hex-ey corners

TylerH• 9 years ago

I understand the concern, but this concern misses the nuance of what 'nature prefers' means.

ebcode• 9 years ago

It's a colloquialism at this point. Nature also abhors a vacuum, goes toe to toe with Nurture, and is a mother herself.

pavlov• 9 years ago

Now I'm imagining Nature as a single mom who likes to decorate her apartment with hexagons, never vacuums, and occasionally invites Nurture to sleep over.

mcnamaratw• 9 years ago

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• 9 years ago

Aren't triangles the strongest shape?

https://math.stackexchange.com/questions/1393965/are-triangl... https://www.reddit.com/r/askscience/comments/619ygo/why_are_...

chii2• 9 years ago

And what do you get when you have lots of triangles packed together?

ecesena2• 9 years ago

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.

35bge57dtjku• 9 years ago

Not when you're pressing in on them from all sides. Look at arches and chicken eggs.

Pulcinella• 9 years ago

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...

jacobolus2• 9 years ago

There are several different criteria you might want to optimize for that result in hexagons, not just close-packing of circles. (Obviously they are somewhat related, but if you step up to 3 dimensions then you start getting different shapes/structures for different criteria, such as a diamond lattice, an FCC lattice (voronoi cells make a tiling by rhombic dodecahedra), a tiling by truncated octahedra, ....)

In particular, bees probably make hexagons because that minimizes the amount of wall you need per area, for a given cell size. If bees were really just making something like a voronoi diagram from somewhat spread out points, you wouldn’t get quite so regular a hexagonal tiling.

I imagine there’s some research about the precise method by which bees build their honeycombs, if anyone wants to go dive into the literature.

stinos2• 9 years ago

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• 9 years ago

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...

[2] http://1.bp.blogspot.com/-uM7ATVMEcDA/TdcWZm9BPEI/AAAAAAAAI8...

dt_rsp• 9 years ago

Jürgen Tautz's "The Buzz about Bees" mentions this.

It says the bees build cylindrical cells around themselves initially, but then raise the temperature of the wax to 37-40 degrees C, when the wax is warm enough to flow into the hexagonal shapes.

(Pages 172-176)

pmurT• 9 years ago

Bees make hexagons. I've seen tons of horizontal and odd shaped burr comb that is still hexagonal - which if they were truly making circles would remain circles as there is no vertical load.

ueliem• 9 years ago

I wonder if it could be related to an insect equivalent of grid cells, neurons involved in dead reckoning found in mammals. The firing pattern of a grid cell is a triangular or hexagonal pattern depending on how you look at it. Drosophila's ellipsoid body neurons have been shown to behave similarly to head direction cells so it's not implausible.

https://en.m.wikipedia.org/wiki/Grid_cell

https://en.m.wikipedia.org/wiki/Head_direction_cells

ecesena2• 9 years ago

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.

tyrw• 9 years ago

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

gaius2• 9 years ago

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

GuiA• 9 years ago

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...

gaius2• 9 years ago

I think downvoters may be unaware of the history of the term: https://en.m.wiktionary.org/wiki/Hexagone

agumonkey• 9 years ago

Quite often I looked at it and saw a Pentagon. Also using the loose hexagone definition, you could probably retrofit it on any point in time anyway :D

jacobr• 9 years ago

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

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

jacquesm2• 9 years ago

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

askvictor• 9 years ago

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

jacquesm2• 9 years ago

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.

tambourine_man• 9 years ago

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

https://youtube.com/watch?v=Pypd_yKGYpA

leke• 9 years ago

And this, also from PBS https://www.youtube.com/watch?v=X8jOxEGVyPo

pseudozach• 9 years ago

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

Why nature prefers hexagons

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