Penrose tiling

Imagine you have a bunch of shapes that look like diamonds. You want to put them together to make a pattern on the floor of your room. But you don't want any gaps, and you don't want them to overlap too much.

Penrose tiling is a special way of putting these diamond shapes together. You start with a big diamond and then cut it up into smaller diamonds in a special way. Then you take those smaller diamonds and put them together again in a special way.

The special thing about Penrose tiling is that it's impossible to make it perfect. No matter how hard you try, there will always be tiny gaps that are impossible to fill. This makes it very interesting and exciting to math people.

Also, the pattern you get from Penrose tiling looks really cool and unique. It's like a maze that you can stare at for a long time and still find new paths.