Scientists have discovered incredibly complex mazes within the atomic structure of quasicrystals. These unusual crystals have atoms arranged in intricate, non-repeating patterns that defy traditional laws of symmetry. Researchers at the University of Bristol in the U.K. developed an algorithm to chart a route that touches every atom in a quasicrystal exactly once.
The resulting diagrams reveal beautiful, maze-like structures that grow exponentially in complexity. When we looked at the shapes of the lines we constructed, we noticed they formed incredibly intricate mazes,” said Felix Flicker, lead author of the study. “The sizes of subsequent mazes grow exponentially — and there are an infinite number of them.”
This breakthrough could have significant implications for various applications, including scanning tunneling microscopy and industrial chemical reactions.
In scanning tunneling microscopy, an ultra-sharp tip is guided over a material to sense atoms one by one, creating an image at the atomic level. Complex images, such as those of quasicrystals, can take up to a month to produce.
Maze-like structures in quasicrystals
However, with a more efficient route, this time could be halved. Flicker also suggests that this discovery could lead to the development of more efficient crystalline catalysts for industrial chemical processes, potentially reducing the costs and time required to produce certain compounds. Our work shows quasicrystals may be better than crystals for some adsorption applications,” said Shobhna Singh, a co-author of the study.
“For example, bendy molecules will find more ways to land on the irregularly arranged atoms of quasicrystals.”
The researchers recreated the structure of quasicrystals using a 2D version of Ammann-Beenker tiling, a type of aperiodic tiling similar to Penrose tiles. They developed an algorithm to find a Hamiltonian cycle over these tiles, effectively representing the arrangement of atoms in quasicrystals. Looking to the future, Flicker believes that new applications of this discovery may emerge over time.
“We’re hoping the most interesting applications are things we haven’t thought of,” he said. The study’s results were published in the journal Physical Review X.
