Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Why nature prefers hexagons

nautil.us

Post reply on HN
Print view View original

21–30 of 64 posts

Re: Why nature prefers hexagons

#21

Post by jacobolus »

Pulcinella wrote: post #17

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…

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.

Re: Why nature prefers hexagons

#22

Post by 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.

Re: Why nature prefers hexagons

#24

Post by robbrown451 »

tzs wrote: post #12
robbrown451 wrote: post #3

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

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 t…

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.

Re: Why nature prefers hexagons

#25

Post by ecesena »

huac wrote: post #10

Aren't triangles the strongest shape? https://math.stackexchange.com/questions/1393965/are-triangl... https://www.reddit.com/r/askscience/comments/619ygo/why_are_...

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.

Re: Why nature prefers hexagons

#26

Post by taeric »

robbrown451 wrote: post #3

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

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.

Re: Why nature prefers hexagons

#27

Post by ebcode »

ineedasername wrote: post #4

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.

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

Re: Why nature prefers hexagons

#28

Post by lightedman »

tzs wrote: post #12
robbrown451 wrote: post #3

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

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 t…

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 .

Re: Why nature prefers hexagons

#30

Post by mjevans »

tzs wrote: post #12
robbrown451 wrote: post #3

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

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 t…

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

Post reply on HN