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Figure 1
The evolution of the distribution function with a consecutive introduction of phason flips to the RPT with a constant probability of the flip α = 0.1. With growing disorder, the distribution at [z_\bot = 0], which is absent in the non-disordered structure, also grows. After l = 200 Monte Carlo steps of flips introduced to a large dataset of RPT positions, the distribution is almost Gaussian. The p5 value, which states what percentage of positions are within the new fifth AS, grows up to 10%. By analysing the norm of the displacement vector rflip (in units normalized by the rhombus edge length) it is evident that phasons are diffusive modes with respect to l that plays the role of time. The distribution of the phason displacement vector shows that the number of possible displacements for randomized tiling is significantly greater than for the one-flip approximation, where there are only two possibilities affined to fft and ftt flips. The colour code for arrows indicating the orientation of the components of the RPT is red for the x axis, green for the y axis and blue for the z axis.

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