Generative Art Geometry. Logical interpretations for Generative Algorithms

This paper tries to identify the creative processes of Generative Art that brings to the construction of dynamic procedures of transformation, generative algorithms, by departing from interpretative logics. This construction becomes possible through a dynamic approach to Geometry. In fact, overcoming the logic of the figures and related rules, this approach opens to the logic of the progressive processes and to the dynamics of transformation inside the geometric space. This dynamic use of Geometry can be performed crossing again the revolution operated by Brunelleschi, by Piero della Francesca and by Leonardo da Vinci. This Renaissance revolution founds on the convergence between Art and Science and on the discovery of the Perspective Logic. The "formella" of Brunelleschi interpreted by P.A.Rossi indicated that Brunelleschi made a peculiar, not casual choice of a point of view, with a distance from Battistero equal to the side of a cube involving the architecture and the optic cone, indicated by the circle, able to have a correct perspective. This was the approach for defining the structure of perspective the "perspective tool". Paolo Alberto Rossi, "La scienza nascosta", (the hidden science). Quoting Decio Gioseffi, "The perspective has been the first mathematical (in systematic and univocal terms) formalization of a "physic" law indefinitely "extensible", of general validity and general verifiability". The perspective, also in the first geometric tools structured by Brunelleschi, is a logical form of representation of the space that allowed, for the first time in human culture, to represent the infinite. The Perspective performs the representation of the infinite identifying a point of view. This means that the complexity of the space is XVII Generative Art Conference GA2014