Bubbles can move freely once created, so they have more freedom than cookies that are stick in place. Thus, bubbles will look for optimal volume to boundary ratio with less constraints
I just woke up with my phone on this. My assumption is that remembering that optimal packing thing just caused me to pass out, presumably to protect myself.
I've legit been thinking about this since i posted the comment lol. I think the target area should probably be a minimal regular hexagon, but I honestly dont have the mathematical chops to figure it out myself or to know which would be more interesting.
Intuition tells me to either try to reduce the problem to like convex hull or figure out a reasonable way to generate random packings and just monte carlo it a few million times for a close to optimal solution. A reasonable way to generate random packings feels like it would be way harder to implement than it sounds
I don't think I've ever seen any household grade ovens really provide even heat, maybe if you use them with the rotating fan thing, but certainly not in standard mode. You need to spend the big bucks on professional kitchen grade stuff for that.
I love making chocolate chip cookies, and have refined my technique so a batch of dough fills my two baking sheets perfectly without them smooshing together. The two tricks are using a little more flour and baking soda than the recipe says, so they're a little fluffier and don't spread out so much, and consistent ball size.
Can also put the tray with cookies on it in the freezer, that can help keep them from spreading as much! Then throw it in the oven from frozen like. Or...firmed up like.
I wonder if this relates to them having six legs somehow. Like, they're able to measure where the next hex should be based on leg length and direction or something.
The bee doesn't have to know anything about numbers to make the honeycomb. All it needs to know is how big to make the circle (bee-sized) and where the circle should be (touching two other circles). From there, the hexagons form naturally.
I suspect having round shape pushing against each other isn't enought to get a hex shape.
In the picture, cookies are tiled such that those in the center are surrounded by 6 other cookies and have a hex shape. Others are surrounded by 2 to 4 cookies and are not hex. So it probably has to do with the tiling.
Notice how they didn't spread the cookies evenly on the tray? If they had, it would've resulted in squares - not hexagons. On the left, some cookies look more like squares already.
Hexagons are just one possible way to tile the plane without gaps. The only reason bees use hexagons is because tiling a plane with hexagons results in the lowest possible total perimeter for equally sized shapes. And bees build the edges of their comb shapes using wax, which is expensive.
Bees literally do not use hexagons, they make roughly round shapes and the force of the surrounding cells compresses them into hexagons. This is called self-organization and it's observable in bubbles as well.
It's not a plane tiling problem; it's a circle packing problem. The optimal euclidean circle packing results in each cookie having six cookies around it, and so when they melt, hexagons.
Bestagon cookies!
They're the hexagreatest!
Hecks a good cookies.
Alright, as long as someone commented it!
https://youtu.be/thOifuHs6eY
ONE. That's how many cookies fit on that tray.
If you're feeling generous you could break off some sections of your one cookie for your friends.
What part would you share? The crispy outer edge, or soft chewy center?
The overcooked back half.
It's so dear of you to assume I have friends. That cookie is all mine, sweetie.
Someone hexed those cookies
The toppings are also cursed.
What have you got against M&M cookies??
Du bist eine hexe
Columnar basalt cookies
This may be my favorite voronoi tesselation.
This only happened because they laid them in rows of 5-4-5-4.
Yeah, it happens when you pack the circles as densely as possible. If you place them in a grid, they will expand to a grid.
I think that depends on the fiction between each item / cell, and the plane.
I think soap bubbles for example will always form hexagons.
Bubbles can move freely once created, so they have more freedom than cookies that are stick in place. Thus, bubbles will look for optimal volume to boundary ratio with less constraints
Thats what i said?
Yes :) since the topic was coming back in another thread, I felt more explanation was nice
Voronoi cookies!
me after discovering the voronoi node:
I wonder what the optimal packing of 17 hexagons looks like
I just woke up with my phone on this. My assumption is that remembering that optimal packing thing just caused me to pass out, presumably to protect myself.
Does it haunt your dreams the same way it haunts mine?
AAAAAAAAAAAAAAAAA
Should the target area be square or should it also be a hexagon?
I've legit been thinking about this since i posted the comment lol. I think the target area should probably be a minimal regular hexagon, but I honestly dont have the mathematical chops to figure it out myself or to know which would be more interesting.
Intuition tells me to either try to reduce the problem to like convex hull or figure out a reasonable way to generate random packings and just monte carlo it a few million times for a close to optimal solution. A reasonable way to generate random packings feels like it would be way harder to implement than it sounds
32
LOL you can see how the back is darker and has this curve. Oven not heating as it should
I don't think I've ever seen any household grade ovens really provide even heat, maybe if you use them with the rotating fan thing, but certainly not in standard mode. You need to spend the big bucks on professional kitchen grade stuff for that.
could also be a shadow?
how do you know that's the back and not the side?
But when I do this all the cookies fall out
I think asking which axis would be the question
I thought that was a shadow 😄
But you can get gooey and crunchy in one batch 🤣
Annnnd now I’m baking cookies
Close hexagonal packing. Rigid cylinders will approximate this as well.
Voronoi cookies!
That pan can fit 21 cookies
It can clearly fit 2⁵ hexagonal cookies!
Isn't it 2⁵?
Edit: disregard, I'm clearly blind. Or dumb. Or both.
Shame about all the pentagons there.
I love making chocolate chip cookies, and have refined my technique so a batch of dough fills my two baking sheets perfectly without them smooshing together. The two tricks are using a little more flour and baking soda than the recipe says, so they're a little fluffier and don't spread out so much, and consistent ball size.
I just fill the pan and use cookie cutters after they're baked.
I eat the scraps.
btw anyone know what the onset signs of diabetes is?
Can also put the tray with cookies on it in the freezer, that can help keep them from spreading as much! Then throw it in the oven from frozen like. Or...firmed up like.
Interesting, but just using a little more flour and baking soda seems simpler.
I do both! I like very thick cookies though.
Off to make some hexacookies. Who wants one?
I wonder if this relates to them having six legs somehow. Like, they're able to measure where the next hex should be based on leg length and direction or something.
The bee doesn't have to know anything about numbers to make the honeycomb. All it needs to know is how big to make the circle (bee-sized) and where the circle should be (touching two other circles). From there, the hexagons form naturally.
Cookie Catan!
I suspect having round shape pushing against each other isn't enought to get a hex shape.
In the picture, cookies are tiled such that those in the center are surrounded by 6 other cookies and have a hex shape. Others are surrounded by 2 to 4 cookies and are not hex. So it probably has to do with the tiling.
No they don't (necessarily))??
Notice how they didn't spread the cookies evenly on the tray? If they had, it would've resulted in squares - not hexagons. On the left, some cookies look more like squares already.
Hexagons are just one possible way to tile the plane without gaps. The only reason bees use hexagons is because tiling a plane with hexagons results in the lowest possible total perimeter for equally sized shapes. And bees build the edges of their comb shapes using wax, which is expensive.
Bees literally do not use hexagons, they make roughly round shapes and the force of the surrounding cells compresses them into hexagons. This is called self-organization and it's observable in bubbles as well.
It's not a plane tiling problem; it's a circle packing problem. The optimal euclidean circle packing results in each cookie having six cookies around it, and so when they melt, hexagons.
Fuck reading instructions. Amirite???