Einstein's Terrain 

For this Playful and Creative Science project, my teammate and I explored the "hat polykite" - a recently discovered shape that can cover a surface without ever creating a repeating pattern. I handled the research on what makes this tile special, looked into how it could be used in real life, and helped build our physical model. My teammate worked on the math theory and helped with laser cutting and putting everything together.

What makes the Einstein tile so interesting is that it breaks the rules of normal tiling. Most tiles create predictable patterns that repeat over and over, but this shape creates infinite unique arrangements that never repeat. We studied how its complex internal structure, made up of smaller triangular pieces with specific rules, keeps it from ever forming the same pattern twice. The math behind it was fascinating, but we wanted to show how it could actually be useful in the real world.

Our creative challenge was turning this abstract math concept into something people could actually see and touch. We built "Einstein's Terrain", a wooden landscape made from over 100 laser-cut Einstein tiles stacked at different heights. The model is about the size of a large book and shows how these non-repeating patterns create more natural-looking terrain than regular geometric grids. By stacking the tiles to create mountains and valleys, we demonstrated how this tiling method could work when used to map out terrains.

The project revealed cool connections between pure math and practical design problems. The Einstein tile follows curved boundaries more naturally than squares or hexagons, which could be huge for terrain simulation. While regular symmetric tiles are easier to work with and more predictable, our terrain model proved that aperiodic tiling creates more organic, realistic landscapes. This project showed me how mathematical breakthroughs can inspire creative solutions across different fields, and how building something with your hands can reveal practical uses that aren't obvious just from studying the theory.