Tessellations of a plane surface by means of unit-sided regular polygons is a classical subject both in art, with examples dating back to the earliest human civilisations, and mathematics, where the complex patterns generated by a very simple set of rules have fascinated generations of inquisitive souls. While several taxonomies of the repeating patterns of a tessellation exist, the mathematical treatment of a particular finite tessellation is a quite recent field, greatly aided by computer algorithms. Introducing Tessella, a free software library of functional algorithms, written in Scala, where finite tessellations are described as immutable undirected planar graphs; thus providing the capabilities to experiment with manual and programmatic creation of finite tessellations, able in turn of inspiring new artistic insights. Abstract paintings are shown as an example, together with ideas on how this exploration journey might be taken further.