A group of scientists may have designed the world’s most difficult maze. The maze, which is highlighted in a new study featured in Physical Review X, was designed using a series of different geometric concepts like Ammann-Beenker tilings and Hamiltonian cycles.
To understand what makes the maze so difficult, you first have to understand those different concepts. Hamiltonian cycles, for example, are essentially like loops through a map that visit all of the stopping points. For instance, imagine a knight on a chessboard. You move it around, two spots forward, one spot back, until it has visited every spot on the board once and only once.
This “Knights Tour” is one of the most classic Hamiltonian cycles, and now the scientists involved in the research have come up with ways to create even larger versions of those cycles using irregular structures like Ammann-Beenker tilings—which are essentially tiling patterns that never repeat. This is the foundation for what they are calling the world’s most difficult maze.
To create the maze, the scientists utilized structures similar to an exotic type of matter we call quasicrystals. These repeat in a pattern, but the pattern doesn’t exactly repeat. Because the quasicrystals “slice through a crystal that live in six dimensions,” they are especially exotic and intricate, which makes them ideal for creating intricate mazes with an infinite number of pathways.
However, quasicrystals are also extremely rare. Only three were found in a meteorite that crashed in Siberia, though a nuclear test in 1945 did see the creation of the world’s first artificial quasicrystal. To create the world’s most difficult maze, the researchers basically employ a Hamiltonian cycle on the quasicrystal, which sees every atom on the crystal visited once.
They call these mazes “fractals,” and they are believed to have unintended side effects, as well, like causing the adsorption of materials. Some have even proved particularly useful at adsorbing carbon dioxide. Unlike absorption, adsorption is when the molecules adhere to a surface, whereas absorbing is when the molecules are dissolved into the surface.
Now, the scientists behind creating what might be the world’s most difficult maze believe they may also be able to turn that maze into a solution for all the extra carbon dioxide we have in the atmosphere, thus helping combat climate change. At least, it’s one possible solution.
