# 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 a mathematical principle, but forms an independent mode of intellectual investigation.

In previous work ideal quilts, or two-dimensional representations of certain numerical sequences associated with special permutation groups, were considered. In this work the relationship between ideal quilts and both: the underlying mathematical concepts and the foundational dada-constructivist ideas is explored. In particular, the aesthetics of ideal quilts is linked to the Marcel Duchamp’s idea of three standard stoppages, where chance is proposed as the universal measuring device to be employed in all visual representations.

The accident is indeed integral to the construction of ideal quilts, as they are precise combinations of the unstructured and the highly structured components. In the present work the balance between these two components is disturbed. This manifests itself in discontinuity and smearing of the diagonal lines in the image. The image is a non-ideal quilt, an exact two-dimensional representation of a particular non-ideal numerical sequence.