A bit too playful for me, but it gets the message across: https://youtube.com/watch?v=Pypd_yKGYpA
And this, also from PBS https://www.youtube.com/watch?v=X8jOxEGVyPo
Why nature prefers hexagons
51–60 of 64 posts
Re: Why nature prefers hexagons
#52Started 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 conscio…
Interesting! My eldest has been working on sketches for a game he calls 'Hex'.
Re: Why nature prefers hexagons
#53Any relation to three-phase power being more efficient than single phase?
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.
Re: Why nature prefers hexagons
#54You 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…
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.
Re: Why nature prefers hexagons
#55Always 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
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.
Re: Why nature prefers hexagons
#56Always 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
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.
Re: Why nature prefers hexagons
#57I 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.
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.
Re: Why nature prefers hexagons
#58Earlier quoted context omitted.
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 .
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…
"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.)
Re: Why nature prefers hexagons
#59Earlier quoted context omitted.
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…
"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 ov…
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.
Re: Why nature prefers hexagons
#60Always 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
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.
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.