The folding of art: avoiding one's past in finite space

Abstract

Through-out human history the new generations have sought to create their own artistic style while trying to avoid repeating, for example, earlier generations' music. If we assume that this search occurs in a multi-dimensional but confined space of creativity, this gives rise to highly complex dynamics. We present a very simple mathematical model with two parameters which can serve as a generic representation for past avoidance in finite space and is qualitatively distinct from earlier dynamical systems. In the presented radially confined form, the trajectory preserves its complexity while retracting to the vicinity of a hypersurface of constant radius when considered in higher dimension.