cookie combs

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.

Cookie Catan!

Bestagon cookies!

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?
Dude, if you get the nachos stuck together, that's one nacho.
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

Sing the song!

🎶 Hexagons are the bestagons

This may be my favorite voronoi tesselation.

Columnar basalt cookies

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.

Voronoi cookies!

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?
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

turn the tray halfway through cooking for god sake

But when I do this all the cookies fall out
- how hard are you spinning
I thought that was a shadow 😄
But you can get gooey and crunchy in one batch 🤣

Annnnd now I’m baking cookies

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.

Voronoi cookies!

Close hexagonal packing. Rigid cylinders will approximate this as well.

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.

Off to make some hexacookies. Who wants one?