# Andrzej K Brodzik

One of the main goals of both science and art is to reveal fundamental principles governing the order of space and time. This task can sometimes be facilitated by juxtaposing structure and randomness, intention and accident. Conceptual and non-objective art that explores these relationships in a deep way, for example, by employing fundamental ideas from number and group theories, does not function merely as a pleasing illustration of mathematical principle, but forms an independent mode of intellectual investigation.

The three images "three graces", "coming together" and "all is one" are parts of a triptych called "stainglasses". The triptych is a homage to Samuel Beckett's play "Rockaby". In "Rockaby" an old woman sits in a rocking chair, next to a window, and reflects on her life. The three stainglasses can be viewed as representations of three alternative life histories, encoded by a combination of cyclic and seemingly random patterns. The mathematical apparatus used to generate these patterns is based on a combinatorial concept called "bat permutation". Despite the simplicity of bat permutation definition, given by the equation i − p(i) mod L ε Perm, many aspects of bat permutation construction remain unresolved. In particular, the structure and the numerics of bat permutations is currently a subject of intense investigation.