Rational approximants to 5, 8 and 7-fold two-dimensional tilings

The strip projection method is used to generate rational approximants to Penrose, octagonal and 7-fold tilings. Two types of approximants to the Penrose tiling are considered, wherein the basis vectors of the approximants are either orthogonal or are 72° apart. Various types of approximants including those with partially retained quasiperiodicity are generated and the pseudosymmetries arising therein analyzed. A simplified approach based on uniform distortions of perpendicular space is put forth for the analyses.