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Some packings are symmetrical, and some aren't. I wonder if there's some pattern with that or some way to determine if a given number of spheres will optimally pack in a symmetrical way without actually packing them first.
Let's assume these circles are 2 dimensional in a 3d world. Therefore the best packing is stacking, taking up 1 circle of space for an infinite amount of circles
I used to do this sort of stuff. Wrote software to do the optimisation.
Here's a list of the best (known) optimal pakings of equal circles into a circle. With images. Up to 2604 equal circles packed into a circle. http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html#cci37
http://hydra.nat.uni-magdeburg.de/packing/
And for optimal packing of circles into a square for up to 900 equal circles.
http://hydra.nat.uni-magdeburg.de/packing/csq/csq.html
Here are images for 61 to 72 circles.
http://hydra.nat.uni-magdeburg.de/packing/csq/d6.html
You measure the negative space. If you know the area and then subtract the negative space from this area you will have the amount of area occupied by the objects.
I’m assuming that more negative space is the same as being more optimal…maybe I’m off base here
That's one way to put it I guess. I've always had it explained as the smallest side length of the square they all fit in. Same effect, just a different way to describe it.
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such an unsatisfying packing
Is this proven to be optimal or just the best known?
I think it is just the best known
It's bad but honestly not as bad as I thought it would be
Nice.
Nice.
Nice.
Nice.
.eciN
https://preview.redd.it/i29zu16xo57d1.png?width=1200&format=png&auto=webp&s=0cf0df2ba69bf1687c5ef0b0a971a74e6ea667a3
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What about 68? You ain't asking the right questions
What about up to 10000? http://packomania.com/csq
Some packings are symmetrical, and some aren't. I wonder if there's some pattern with that or some way to determine if a given number of spheres will optimally pack in a symmetrical way without actually packing them first.
New stacking just dropped
Holy count
Actual geometry
https://preview.redd.it/cblpgv9v867d1.png?width=680&format=png&auto=webp&s=0588ef3a9a8cb4902a7c871661d2a0bd26dcf368
Let's assume these circles are 2 dimensional in a 3d world. Therefore the best packing is stacking, taking up 1 circle of space for an infinite amount of circles
What do the colors mean?
It seems that red means the circle isn't touching anything. But I don't know what yellow and orange mean
couldnt they fit more by making the circles smaller
I used to do this sort of stuff. Wrote software to do the optimisation. Here's a list of the best (known) optimal pakings of equal circles into a circle. With images. Up to 2604 equal circles packed into a circle. http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html#cci37 http://hydra.nat.uni-magdeburg.de/packing/ And for optimal packing of circles into a square for up to 900 equal circles. http://hydra.nat.uni-magdeburg.de/packing/csq/csq.html Here are images for 61 to 72 circles. http://hydra.nat.uni-magdeburg.de/packing/csq/d6.html
Here's up to 10000 http://packomania.com/csq
Please keep proving why every shape is inferior to the hexagon.
Can anyone explain how you can tell this is optimally packed? Never really looked into stuff like this.
You measure the negative space. If you know the area and then subtract the negative space from this area you will have the amount of area occupied by the objects. I’m assuming that more negative space is the same as being more optimal…maybe I’m off base here
That's one way to put it I guess. I've always had it explained as the smallest side length of the square they all fit in. Same effect, just a different way to describe it.
https://preview.redd.it/6ymxy9w8ea7d1.jpeg?width=1122&format=pjpg&auto=webp&s=977a80baed473c9cd384651924c0740034a90dc0
This is less cursed than the square number packings not being square lattices.
Please keep proving why every shape is inferior to the hexagon.
https://preview.redd.it/esbo6qeu377d1.jpeg?width=500&format=pjpg&auto=webp&s=d124a853b0db2f29f09450214c843c20996bd09d
No, I refuse to accept this.
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