# Generative Art Geometry. Logical interpretations for Generative Algorithms

## Reference

Celestino Soddu: Generative Art Geometry. Logical interpretations for Generative Algorithms. In: Generative Art 2014.

## Abstract

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.

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 scientifically investigable through the subjectivity of an observer and his Logical Interpretations. The scientific search, in fact, can follow too the same interpretative way pointed out by the perspective. Until now, as shown by Einstein and his logical interpretation of the universe through the theory of Relativity, together with Max Planck and his quantum theory that is a different logical interpretation of the universe. Both theories are useful and true, also if so in contrast one each other. The points of view are different but the matter is the same.

Generative Art pursues this interpretative approach. And it does it redrawing its tools starting from the main one, the Geometry. The interpretative logics, activated by Generative Art, build parallel, multiple and progressive paths of dynamic transformations. These are managed through algorithmic logics.

The Generative Geometry really becomes one of the main tool of Generative Art because it is able to logically represent the interpretation of the author performing his artworks in the endless multiplicity of the possible variations.

The act of writing Generative Algorithms is representing and investigating the existing environment from different and progressive logical points of view, tracing the rules for transforming it from the past into the future.

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