Critique and a Science for the Sake of Art: Fractals and the Visual Arts

J^ D rawing attention to the Kantian aesthetic that underpins Benoit Mandelbrot's [1] argument for 'an art for the sake of science' does not represent a sufficiently critical engagement of fractal geometry's entry into visual discourse (an entry made largely transparent by the suggestion that art acts as a handmaiden to science). Merely pointing to the extent of this aesthetic debt leaves the necessity for its adoption unexplored. It also leaves fractal imagery outside the orbit of contemporary visual critique by affording an unproblematic status to this geometry's intervention. This status is made possible by the fact that a transcendental aesthetic, in its traditional form, displaces any notion of a critical visual practice by reducing all engagements of the visual to judgments of taste [2]. The necessity of adopting this aesthetic is apparent in the claims that first emerge in Mandelbrot's remarkable and impressive book The Fractal Geometry of Nature [3] and later reappear, though often only by implication, in his Leonardo article. Indeed, the title of this earlier work indicates the truth value Mandelbrot ascribes to his discourse. Namely, the implication is that nature's truth is fractal geometry: the geometry of chance and change, the geometry of the vernacular, the measuring of the everyday. (Fractal images have, in part, a descriptive role in the dissemination of this truth.) The basic concepts that Mandelbrot advances for fractal geometry, as points of differentiation from traditional geometry, can be broken down into two categories: those related to the generative concepts that inform his practice and those connected to the resultant aesthetic and truth value conclusions drawn from this practice.