Physicists have designed what they believe to be the most challenging maze ever created, leveraging a pattern from the game of chess. This intricate maze, resembling a complex snowflake at first glance, presents a formidable challenge for puzzle enthusiasts.
The maze is constructed using a Hamiltonian cycle, a graph cycle that visits every node exactly once. This movement pattern mirrors the “Knight’s Tour” in chess, where a knight can visit every square on the board once without repetition, eventually returning to its starting position.
The physicists’ maze utilizes a similar principle, assembling Hamiltonian cycles within quasicrystals. Quasicrystals are unique materials. Unlike regular crystals with periodically repeating structures, quasicrystals exhibit non-repeating, asymmetric patterns. These unusual structures create perplexing three-dimensional forms and almost magical properties in other dimensions. A 2022 study demonstrated enhanced quantum system coherence by applying a quasicrystalline pattern to atoms using lasers, effectively creating a quasicrystal in time.
A familiar example of a 3D quasicrystal is the icosahedron, a 20-sided figure resembling a soccer ball. The shift from periodic to quasi-periodic structures dramatically expands the possibilities of symmetry, allowing for previously forbidden symmetries like the icosahedron.
Quasicrystals rarely form naturally on Earth. Some have been discovered in lonsdaleite, a mineral harder than diamond found in meteorites. Interestingly, quasicrystals also formed in trinitite, the glassy material created during the 1945 Trinity nuclear test.
The research team developed an algorithm to construct Hamiltonian graph cycles on two-dimensional Ammann-Beenker tilings. These 2D mazes demonstrate Hamiltonian cycles mimicking the atomic arrangements within quasicrystals. This approach simplifies seemingly complex problems within these specific quasicrystalline structures.
The research, detailed in a paper accepted for publication in Physical Review X, highlights the maze’s exponential growth in size and infinite variations. This intricate pattern has practical scientific applications. For instance, the Hamiltonian cycle offers the most efficient path for microscopic imaging devices like scanning tunneling microscopes. Additionally, quasicrystals have implications for various physics problems, including protein folding models.
Beyond its scientific relevance, this research offers a fascinating glimpse into how mathematics can reveal the exotic patterns hidden within our universe. The seemingly simple act of creating a complex maze unlocks a deeper understanding of quasicrystals and their potential.
