Abstract： Based on the spectral structure of a class of one-dimensional three-tile quasiperiodic lattice models that are established in 1990 for which the (concurrent) substitution rules are S → M, M → L, and L → LS, with S, M, and L representing the short, medium, and long tiles of atomic spacings, respectively, we suggest that S is E (egg), M is SI (silkworm) and L is M (moth), for easily understanding. By the use of the number theory, we have rigorously proven the existence of the limit θ = limn → ∞ Sn-1/Sn ≈ 0.68232789 ..., where Sn is the number of elements contained in the n-th silk sequence. Some relations among the sequences En, SIn, and Mn are found, where the subscript n means the n-th generation.
LUAN Chang-Fu. Some Invariants of the Silk Quasi-lattices[J]. 中国物理快报, 2003, 20(2): 267-268.
LUAN Chang-Fu. Some Invariants of the Silk Quasi-lattices. Chin. Phys. Lett., 2003, 20(2): 267-268.
2003, Vol. 20 
