Elliptic tiling

Elliptic tiling is like playing with Legos, but instead of building a tower, you use different shapes to fill up a whole bunch of space.

Imagine there is a flat piece of paper with a circular shape on it. Now divide the circle into equal parts like a pie (these are called slices). Next, cut each slice into smaller pieces, like you are making little pizza slices out of these slices. You can rearrange these smaller slices and create many different patterns that fit together perfectly to cover the entire circular shape like a puzzle.

Now here's the tricky part: instead of using a circle, imagine using a shape that is stretched or squeezed in a certain way, like stretching a rubber band in different directions. These shapes are called ellipses. When you cut the ellipses like the circle slices, you might not end up with perfect little pizza slices. That's okay because you can use different shapes to cover up the edges.

Elliptic tiling is simply this process of fitting together different shapes to cover the entire ellipse, and it can create all kinds of beautiful patterns that repeat forever.