Combination of commensurate and incommensurate periodic substructures

The resulting (A + T) sequence is perfectly ordered (its diffraction pattern would be built by peaks ) but it is not periodic (the two periods a and ar/2 are incommensurate) (See Fig. 3.45). Approximations to this composite structure may be built considering the representation of r through a continuous infinite fraction  

By substituting in the sequence T (having period aril) the values r0, rb r2, etc., we obtain the periodic structures T() (period all), 1 (period a), TTiperiod a3/4), 7) (period a5/6), T4 (period a8/10), etc. These structures superimposed to (combined with) structure A give rise to a series of (periodic, commensurate) approximants of 

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