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Abstract
The reference lattice concept 1 has been successfully used to calculate the scaling exponents for intensities of singular diffraction component of the one-dimensional Thue-Morse sequence at positions indexed by 1/p, where p is a prime number, and especially for p = 17 and 41. Based on the average unit cell approach 1 the probability distribution of atomic displacements from the reference lattice points has been obtained. Specially defined δ-parameters significantly reduce the number of variables required for the structure factor calculation. Values of fractal exponents for scaling of diffraction intensities with the number of atoms have been checked numerically for numbers of atoms reaching 232.
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