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

TL;DR

This paper introduces a simple mathematical model to represent how human artists avoid repeating past styles within a finite creative space, capturing complex dynamics and the tendency to stay near a constant-radius hypersurface.

Contribution

It presents a novel, minimalistic dynamical system model for past avoidance in finite multidimensional creative spaces, distinct from previous models.

Findings

Model captures complex trajectories in confined spaces.

Trajectories tend to stay near a hypersurface of constant radius.

The model is qualitatively distinct from earlier dynamical systems.

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.