Physicists Have Created The World's Most Fiendishly Difficult Maze

A team of physicists, led by Felix Flicker from the University of Bristol in the UK, have created the most intricate maze ever devised, inspired by the strategic game of chess and the principles of fractal geometry. They achieved this by generating Hamiltonian cycles in patterns known as Ammann-Beenker tilings, which are used to describe an exotic form of matter known as quasicrystals.

Quasicrystals are a rare form of matter found in nature, with atoms arranged in a pattern that does not repeat perfectly. They are a strange hybrid of ordered and disordered crystals, falling between the regularity of an ordered crystal (such as salt or diamonds) and the randomness of a disordered solid (like glass or certain forms of ice).

The creation of Hamiltonian cycles in Ammann-Beenker tilings is reminiscent of a Knight’s tour in chess, where the chess piece visits every square on the board only once before returning to its starting square. The generated cycles visit each atom in the quasicrystal only once, connecting all the atoms in a single line that never crosses itself, and can be scaled infinitely to create a fractal pattern.

The implications of this research extend beyond creating complex mazes. Finding Hamiltonian cycles is extremely difficult, and a solution that would allow for their identification could potentially solve other complex mathematical problems, such as route finding systems and protein folding.

Interestingly, quasicrystals may also be better than crystals for certain adsorption applications. Quasicrystals have a larger surface area for adsorption due to their brittle nature, which allows them to break into tiny grains. Furthermore, bendy molecules can find more ways to land on the irregularly arranged atoms of quasicrystals, potentially making them more effective for carbon capture via adsorption.

The research has been published in Physical Review X. If you have a minotaur you need to hide away, this team of physicists might just have the solution.

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