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Taking principles from fractal geometry and the strategic game of chess, they have created what they say is the most fiendishly difficult maze ever devised.
Led by physicist Felix Flicker of the University of Bristol in the UK, the group has generated routes called Hamiltonian cycles in patterns known as Ammann-Beenker tilings, producing complex fractal mazes that, they say, describe an exotic form of matter known as quasicrystals."When we looked at the shapes of the lines we constructed, we noticed they formed incredibly intricate mazes.
An Ammann-Beenker tiling with a thicker black line tracing out the Hamiltonian path by visiting each vertex. The purple lines are not part of the tiling. (Singh et al.,Their generated cycles visit each atom in the quasicrystal only once, connecting all the atoms in a single line that never crosses itself, but cleanly continues from beginning to end.
For one, finding Hamiltonian cycles is extremely difficult. A solution that would allow for Hamiltonians to be identified has the potential to solve many other tricky mathematical problems, from complex route finding systems to protein folding., an industrial process that involves hoovering up molecules in a fluid by sticking them to crystals.
"For example, bendy molecules will find more ways to land on the irregularly arranged atoms of quasicrystals. Quasicrystals are also brittle, meaning they readily break into tiny grains. This maximizes their surface area for adsorption."
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