Non-local growth of Penrose tilings

The problem of mistakes in Penrose tilings will be investigated. Specifically, we will consider the non-locality of any growth process that attempts to avoid errors in the construction of a tiling of the plane by Penrose rhombs. This discussion will be framed by considering the one dimensional version of this problem for Fibonacci Tilings, the aperiodic tilings of the line. These considerations lead to the conclusion that local growth algorithms for correct Penrose tilings of the plane do not exist.Science, Faculty ofMathematics, Department ofGraduat