Discrete quasiperiodic sets with predefined covering cluster
arXiv:math-ph/0505005 · doi:10.1080/14786430500263413
Abstract
Some of the most remarkable tilings and discrete quasiperiodic sets used in quasicrystal physics can be obtained by using strip projection method in a superspace of dimension four, five or six, and the projection of a unit hypercube as a window of selection. We present some mathematical results which allow one to use this very elegant method in superspaces of dimension much higher, and to generate discrete quasiperiodic sets with a more complicated local structure by starting from the corresponding covering cluster. Hundreds of points of these sets can be obtained in only a few minutes by using our computer programs.
Paper accepted for publication in Philosophical Magazine. Software for quasicrystals available at http://fpcm5.fizica.unibuc.ro/~ncotfas/