Scientists develop world’s most complex maze inspired by chess

In a groundbreaking study, physicists have harnessed the complexity of chess to design intricate mazes that could help solve some of the world’s most pressing problems. These unique mazes, inspired by the movements of a knight on a chessboard, could help address challenges such as industrial processes, carbon capture and fertilizer production.

Lead researcher Dr Felix Flicker, Associate Professor of Physics at the University of Bristol, explained: We noticed that the shapes of the lines we constructed formed incredibly complex mazes. The size of these mazes increases exponentially and there are an infinite number of them.

A Knights Tour The circuit involves the chess piece moving in an L-shape, visiting each square on the board exactly once before returning to its starting point. This circuit illustrates a “Hamiltonian cycle,” a path that visits each point once. Theoretical physicists at the University of Bristol have constructed infinitely large Hamiltonian cycles in irregular structures representing an exotic form of matter called quasicrystals.

Quasicrystals differ from ordinary crystals like salt or quartz because their atomic patterns do not repeat at regular intervals. Instead, they can be described mathematically as six-dimensional crystal slices. Natural quasicrystals have only been discovered in a single Siberian meteorite, while the first artificial quasicrystal was accidentally created during the 1945 Trinity test, the atomic bomb explosion depicted in Oppenheimer.

The group’s Hamiltonian cycles visit each atom on the surface of certain quasicrystals exactly once, creating particularly complex mazes described by “fractals.” These paths allow an atomically sharp pencil to trace straight lines connecting all neighboring atoms without lifting or crossing. This is beneficial for “scanning tunneling microscopy,” where the pencil represents a microscope tip capturing images of individual atoms. Hamiltonian cycles provide the fastest possible routes for the microscope, which is crucial because producing a first-order image can take a month.

Solving Hamiltonian cycles in general settings is a huge challenge and could solve many important unsolved problems in the mathematical sciences. Dr. Flicker noted: Some quasicrystals are a special case where the problem is surprisingly simple. This allows for solving seemingly impossible problems, which can be used for practical purposes in various scientific fields.

For example, adsorption involves the adhesion of molecules to the surface of crystals and is essential in industrial processes. Currently, only crystals are used for industrial-scale adsorption. If the surface atoms admit a Hamiltonian cycle, flexible molecules of suitable size can efficiently stack along these atomic labyrinths. Research shows that quasicrystals can be very efficient adsorbers, which is important for carbon capture and storage to avoid CO2 emissions.

Shobhna Singh, co-author and PhD student in physics at Cardiff University, said: Quasicrystals can be more effective than crystals for some adsorption applications. Flexible molecules will find more ways to land on the irregularly arranged atoms of quasicrystals. They are also brittle, meaning they break into tiny grains, maximizing their adsorption surface area.

The efficient adsorption also suggests that quasicrystals could be effective catalysts, improving industrial efficiency by reducing the energy required for chemical reactions. For example, adsorption is crucial in the Haber process, used to produce ammonia fertilizer for agriculture.