# 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.

The two images "coming together" and "all is one" are parts of a series called "stainglasses". The series is a homage to the Samuel Beckett's play "Rockaby". The stainglasses can be viewed as representations of alternative life histories of the character of the play, encoded by a combination of cyclic and seemingly random patterns.

The mathematical apparatus used to generate these patterns is based on a group-theoretic concept called "bat permutation". Despite the simplicity of the bat permutation condition, which requires that the difference between the index sequence and the bat permutation, taken modulo the length of the bat permutation, is a permutation, many aspects of bat permutation construction remain unresolved. In particular, the structure and the numerics of bat permutations is currently a subject of an intense investigation.