This intricate maze connects the dots on quasicrystal surfaces

This maze of jagged curls looks for illustration thing retired of nan world’s hardest puzzle book. How accelerated do you deliberation you tin lick it?

Stuck? Don’t worry. It’s really much of a link nan dots puzzle.

The labyrinthine achromatic way is nan shortest nonintersecting way to link each constituent connected a kaleidoscopic, “quasicrystalline” surface, researchers study July 10 successful Physical Review X.

Shobhna Singh, a theoretical physicist astatine Cardiff University successful Wales and her colleagues examined a type of shape known arsenic an Ammann-Beenker tiling, which fills a two-dimensional abstraction utilizing square- and rhombus-shaped tiles. Like immoderate kaleidoscope images, Amman-Beenker tilings are organized but nan shape doesn’t repetition itself regularly. The atoms successful definite types of quasicrystals — ordered but nonrepeating chemic structures — adopt a akin geometry (SN: 10/5/11).

In an Ammann-Beenker tiling (one shown), squares and rhombuses capable a 2-D abstraction pinch an organized shape that doesn’t perfectly repetition itself.Claudio Rocchini/Wikimedia (CC BY 3.0)

The researchers recovered a way that touches connected each vertex successful an Amman-Beenker tiling, without crossing itself, earlier ending backmost wherever it started. Called Hamiltonian cycles, these pathways shape a closed loop that you tin trace without picking up your finger.

Solving a Hamiltonian rhythm for moreover 1 type of tiling is nary mini feat. But this peculiar rhythm — and perchance others — could thief reside technological challenges. For example, it could make definite quasicrystals much businesslike catalysts, substances that trim nan power required for a chemic reaction. In theory, if molecules progressive successful nan guidance arranged themselves on nan Hamiltonian way of specified a quasicrystal, they could connect to nan aboveground pinch maximum efficiency.

Moving forward, nan squad will hunt for Hamiltonian cycles connected different types of tilings, Singh says. They’re besides looking for caller ways to use their Hamiltonian rhythm to existing challenges. “The astir absorbing exertion could beryllium 1 which we person not thought about.”