On perturbation of aesthetic curves

Abstract

<abstract><p>The notion of aesthetic curve plays an essential role in the generation of aesthetic forms. In order to quantify the aesthetics in art and science some aesthetic standards were introduced but, the beauty is perceived by people in various ways. Bearing this idea in mind, we introduce in this paper the notion of an approximate aesthetic curve by perturbing the equation that defines it. Moreover, we study the relation between the solutions of the perturbed equation and the solutions of the exact equation. For the equation of neutral curves, some stability results in Ulam sense are obtained. We prove that the equation of aesthetic curves by perturbations to an equation for convergent curves is Ulam stable, while by perturbation to an equation for divergent curves, it is not Ulam stable.</p></abstract>