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absolutely continuous algebraic almost-periodic alphabet approximation atomic surface automatic sequences automaton automorphism Borel set coefficients complexity compute consider corresponding crystal curve decurving operations defects defined definition Dekking denoted density diffraction dimension disclinations discrete dislocations dragon curves dynamical system edges eigenvalue eigenvector entropy equation ergodic example exists Fibonacci sequence finite fixed point forbidden planes Fourier transform frequencies function given homotopy infinite sequence integer intersection invariant iteration lattice periodic Lebesgue measure length matching rules Math matrix Mendes France metric tensor modulated morphism multimetrical oblique tiling obtained octagonal tiling one-dimensional paperfolding paperfolding sequence phase phason Phys physical Pisot point group positive potential projection properties Prouhet-Thue-Morse sequence quasicrystals quasiperiodic quasiperiodic tiling Queffelec random result Rivier Rudin-Shapiro sequence singular continuous space group spectral measure spectrum substitution superspace symmetry theorem theory Thue-Morse Thue-Morse sequence topological trace map triangle unit cell vector vertex vertices word