Luis Alvarez Universidad de Las Palmas de Gran Canaria In the course of the history of art we can find artistic expressions that can be understandable in terms of geometric compositions where a number of objects are organized following some composition rules and basic geometric transformations. In this work we are interested in the formalization of such generation principles in such a way that the artistic expression could be interpreted as a particular instance of a formal procedure which provides an algorithm being able to generate images following the same composition principles. We point out that our objective is not to reproduce a literal copy of a particular artistic expression, our objective is to study the mathematical formalization of the composition rules and the design of image generator algorithms accordingly with the composition rules. In this work we study a variety of artistic expressions created by the human being from the prehistoric art (9000 years ago) to the modern art. We try (when it is possible) to identify the composition principles and we design algorithms to generate new images using such principles and random sampling procedures.