Why nature prefers hexagons
nautil.us
nautil.us
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...
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.
[1] http://www.localhoney.co.uk/wp-content/uploads/2010/06/start...
[2] http://1.bp.blogspot.com/-uM7ATVMEcDA/TdcWZm9BPEI/AAAAAAAAI8...
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)
Otherwise, the descriptor is not just imprecise, it is also misleading.
I get it, it's just hard to avoid in English, but it is still a (small) failure in clear science communication.
"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 -- caution, course language
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"
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.
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.
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?
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.)
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.
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
x = r cos (theta) y = r sin (theta)
when you vary r so it gives you a spiral instead of a circle. So it shouldn't be too hard to generate the signals required.
Or there could be a different arrangement of the beam deflectors that didn't give you independent control of X and y.
Same with the timing of the sweep circuits, which only need to hold sync for a single line of video.
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.
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.
https://math.stackexchange.com/questions/1393965/are-triangl... https://www.reddit.com/r/askscience/comments/619ygo/why_are_...
So hexagons are better than triangles, and dodecahedron would be even better, etc. but nature tends to simplicity.
https://upload.wikimedia.org/wikipedia/commons/a/ae/Frontier...
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.
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.