Combinatorial Artists: Counting, Permutations, and Other Discrete Structures in Art

This chapter is motivated by a question I asked myself: “How can combinatorial structures be used in a work of art?” Immediately, other questions arose: Are there artists that work or think combinatorially? If so, what works have they produced in this way? What are the similarities and differences between artworks produced using combinatorics? Combinatorics is a very transversal branch of mathematics. It is connected to logic, and it intervenes in the building of languages in general as natural language, musical language, and poetry. Combinatorics has been present in artistic practice for millenia, especially in music and poetry; for instance, in the shaped poems of Simmias of Rhodes in Ancient Greece. However, we are interested in artistic practices that are driven by the use of combinatorial ideas, structures, and methodologies, artists whose work is conceptualized or merely inspired by combinatorics. This often happens in connection with an interest in structure and language, and the phenomenon was significant in the twentieth century, as a by-product of the revolution that took place not only in art but in many other areas of knowledge. In this chapter, we present a survey of artists that think combinatorially, work combinatorially, and construct combinatorial artworks. The selection covers music, literature, visual arts including digital art, and an example of early physical interactive art, dance, theatre, and cinema. It is a non-exhaustive list of artists, selected to show differences and similarities in their ways of approaching art when using combinatorics.