Crystalline and non-crystalline growth of two-dimensional square-triangle lattices

We have studied the possible structures of two-dimensional lattices composed of squares and equilateral triangles obtained by a coherent way of growing them. The model of growth uses the Stochastic Matrix Method, which is based on the concept of statistical agglomeration of elementary units. The studied lattices satisfy two conditions, they are free of voids and defects and they conserve the relative concentration of elementary units before and after the growth process. In order to compare our results with some specific tilings, we also define an algorithm to construct crystalline families of a given symmetry.