Hey kiddo, have you ever played with building blocks? You know how you can put them together to make different shapes and patterns? Well, imagine if you had some special blocks that could fit together in a really cool way to make a pattern that never repeats. That's kind of like what the ammann-beenker tiling is!
Basically, it's a pattern made up of different shapes that fit together in a certain way. These shapes are called "tiles" and they are all the same shape and size. They look like little hexagons with triangles stuck on the sides.
When you put these tiles together, they form a pattern that never repeats. That means you could look at it for a really long time and never see the same thing twice! It's kind of like a really cool puzzle that you can stare at and try to figure out.
Now, this pattern is named after two people - Ammann and Beenker - who were mathematicians that came up with this idea. They figured out how to make these special shapes fit together in a way that makes the pattern never repeat.
So, there you have it! The ammann-beenker tiling is a super cool pattern made up of special shapes that fit together in a unique way. It's a fun puzzle to look at and try to figure out, and it's named after two smart mathematicians who came up with the idea. Pretty neat, huh?