Tessellations with the modular group from dynamics

Abstract

Automatic generation of coloured patterns with symmetry of the modular group is considered from a dynamical system's point of view. An equivariance property is imposed on dynamical systems to exhibit the required symmetry. The convergence time of an orbit of the dynamical system is used to determine the colour of the initial point. A new and fast algorithm is also presented for the construction of the equivariant system. This method is able to create a great variety of artistic symmetrical patterns.