Settling into a honeycomb
Why slow cooling makes neat patterns, and why six neighbors is the magic number.
What you are looking at
The dots slow down. Small neat patches appear and grow, where each dot has six neighbors in a ring. The patches spread until most of the screen is a honeycomb pattern.
The idea
Put a pile of identical coins on a table and push them together. They settle into rows, and each coin ends up touching six others. That is the way to fit the most coins in the least space.
When things are hot and shaking a lot, they cannot hold that pattern. As they cool and the shaking calms down, they can finally settle into it. A neat patch starts in one spot, and more dots join it, like a crowd forming a line.
If you cool too fast, patches start in many places at once and do not line up with each other. You get a patchwork with seams between them. Slow cooling gives you bigger, neater patches.
Where else you see it
- Snowflakes and ice have six-sided shapes.
- Metal is made of tiny crystal patches (grains). The size of the patches changes how strong the metal is.
- Honeycombs and basalt rock columns also have six sides, though they form for other reasons.
Go deeper: the proper names and the math
The hexagonal arrangement of equal circles covers about π / (2√3) ≈ 90.7% of the plane, which is proven to be the maximum for any arrangement of equal circles (Thue 1890, with a complete proof by Fejes Tóth in 1940).
Crystals grow by nucleation and growth: a small ordered cluster has to reach a critical size before it keeps growing. Many nuclei mean many grains, with grain boundaries between them. Cooling rate controls the grain size, which is a basic tool in metallurgy.