Software

1. Averagero .Program in Mathematica, draw quasiperiodic, specially Penrose tilings using a simple interface.
2. Penrose. Same very simple program in FORTRAN 77 to generate Penrose and other quasiperiodic tilings. Contains documentation and FAQ about tilings.

THESE ARE THE SIMPLEST PROGRAMS TO GENERATE QUASIPERIODIC TILINGS. As default parameters, the programs generate a Penrose tiling, but other isomorphism classes are available by changing the parameters. The program gives some pictures of the generated tilings, and outputs a file with the VERTEX positions. Written as a Notebook in MATHEMATICA and FORTRAN, the programs also allow to obtain the average structure and the corresponding diffraction pattern. Made from our analytical recipe to get the vertex positions as described in: “Analytical expressions for the vertex coordinates of quasiperiodic lattices”, by G. Naumis, J.L. Aragón, Z. Kristallogr. (2003) 218 397, which to our knowledge is the only analytical formula to get the positions in a quasicrystal without any search procedure; the formula is just a generalization of how the vertex positions are found in a crystal: by making integer linear combinations of basis vectors. The simple trick is to use a floor function to generate these linear combinations. Many important results are obtained using this recipe (see G.G. Naumis, “Phason hierarchy and electronic stability of quasicrystals”, Phys, Rev. B71, 144204 (2005). It can be easily generalized in 3 dimensions. Important notice: each time that the parameters are changed in the Mathematica version, one needs to quit and run mathematica again. This bug soon will be fixed.

3. Cass2: Notebook in MATHEMATICA for generating quasiperiodic lattices in 2dimensions using the most general analytical expressions that were developed in: “Analitical expressions for the vertex coordinates of quasiperiodic lattices”, G.G. Naumis, J.L. Aragón, Z. Kristallogr. (2003) 218 397. Therein you will find the notation and the algorithm. This program contains Averagero as a particular case, but contains much more parameters and thus freedom. This program is able to generate very rare and interesting lattices!! Important notice: each time that the parameters of the grids are changed, one needs to quit and run mathematica again. This bug soon will be fixed.