Scientists have created the world’s most amazing maze with future potential to increase carbon capture

In new research, physicists have harnessed the power of chess to create a group of complex mazes that could eventually be used to solve some of the world’s most pressing challenges.

Their unique labyrinthine creations, inspired by the movements of a knight on a chessboard, could help unravel other notoriously difficult problems, including simplifying industrial processes from carbon capture to fertilizer production. The study has been accepted for publication Physical overview X and is published on arXiv prepress server.

Lead author Dr. Felix Flicker, associate professor of physics at the University of Bristol, said: “When we looked at the line shapes we constructed, we noticed that they form incredibly complex mazes. The sizes of the subsequent mazes grow exponentially – and there are an infinite number of them.”

In a knight’s tour, a chess piece (which jumps two squares forward and one right) visits each square of the board only once before returning to its starting square. This is an example of a “Hamiltonian cycle” – a loop over the map that visits all stopping points only once.

Theoretical physicists led by the University of Bristol have constructed an infinity of ever-larger Hamiltonian cycles in the irregular structures that describe exotic matter known as quasicrystals.

The atoms in quasicrystals are arranged differently from the atoms in crystals such as salt or quartz. While atoms in crystals repeat at regular intervals like squares on a chessboard, quasi-crystal atoms do not.

Instead, they do something rather more mysterious: quasicrystals can be mathematically described as slices of crystals that live in six dimensions, as opposed to the three dimensions of our known universe.

Only three natural quasi-crystals have been found so far, all in the same Siberian meteorite. The first artificial quasi-crystal was created accidentally in the 1945 Trinity Test, an atomic bomb explosion dramatized in the film Oppenheimer.

Hamiltonian cycles of the group visit each atom on the surface of certain quasicrystals exactly once. The resulting paths form uniquely complex mazes described by mathematical objects called “fractals”.

These paths have the peculiar property that an atomically sharp pencil could draw straight lines connecting all neighboring atoms without the pencil lifting or the line crossing itself. This has applications in a process known as scanning tunneling microscopy, where a pencil is an atomically sharp microscope tip capable of imaging individual atoms.

Hamiltonian cycles form the fastest possible path that a microscope can follow. This is useful because it can take a month to produce an image from state-of-the-art scanning tunneling microscopy.

The problem of finding Hamiltonian cycles under general conditions is so difficult that its solution would automatically solve many important problems that have not yet been overcome in the mathematical sciences.

Dr. Flicker added: “We show that certain quasicrystals represent a special case in which the problem is unexpectedly simple. In this setting, we therefore make some seemingly impossible problems solvable. This could have practical purposes spanning various fields of science.”

For example, adsorption is a key industrial process in which molecules adhere to the surface of crystals. So far, only crystals are used industrially for adsorption. If the surface atoms admit a Hamiltonian cycle, flexible molecules of the right size can pack with perfect efficiency by lying along these atomic mazes.

Research results show that quasicrystals can be highly effective adsorbers. One use of adsorption is carbon capture and storage in which CO₂ molecules are prevented from entering the atmosphere.

Co-authored by Shobhna Singh, Ph.D. physics researcher at Cardiff University said: “Our work also shows that quasicrystals may be better than crystals for some adsorption applications. For example, flexible molecules find more ways to land on the irregularly arranged atoms of quasicrystals. Quasicrystals are also brittle, meaning they easily break down into tiny particles, which maximizes their surface area for adsorption.”

Efficient adsorption could also make quasicrystals surprising candidates for catalysts that increase industrial efficiency by lowering the energy of chemical reactions. For example, adsorption is a key step in the Haber catalysis process used to produce ammonia fertilizer for agriculture.