Automatic generation of nonperiodic patterns from dynamical systems

A new and fast algorithm is presented in this paper for the automatic generation of aesthetic patterns on nonperiodic tilings by means of dynamical systems. The Chair and the Sphinx tilings are used as illustrations. Invariant mappings are constructed for the creation of striking patterns on these tilings. A modified convergence time scheme is described to enhance the artistic appeal of generated images. This algorithm can be used to create a great variety of exotic patterns with various nonperiodicities.