The CNN Paradigm: Shapes and Complexity

Shapes are the fundamental attribute of visible objects; they give us the perception of structure. They also represent the alphabet of art [Arnheim, 1974]. Shapes represent the object of visible beauty. It is well known that the mathematics of shape and space is geometry. Which is the relationship between dynamical systems and shapes? Could the mathematics of nonlinear dynamics help us to establish an innovative way to go in depth into the world of shape generation? The human mind process of creating shapes is of course a dynamical process and often its complexity involves more steps in combining emergent conditions. The shape generation in the human mind leads often to the emergence status of mental states and the brain-mind complexity is related also to its shape organization process. Some artistic experiences and painters of the last century are taken as examples of the previous concepts. The painter Joan Miró reached the third dimension in his “Still Life with Old Shoe” [Lynton, 1994] that represents a bifurcation point in the production of the artist whose previous paintings were characterized by subjects spatially represented in two dimensions. This fact indicates in the artist’s mind a possible rearrangement of his shape archetypes. Moreover, in the Still Life with Old Shoe the idea of broken forms typical of the period of analytical Cubism appears. The broken forms, like bursts, are evident in the Salvator Daĺı art and in particular in Tête Raphaelesque Éclatée. The dynamical trends of Giorgio De Chirico’s artistic life are well known: he founded with Carlo Carrà the Methaphysical Painting. Surrealists honored his early paintings, but in the Twenties he switched to a Renaissance-based Classicism. He completed his artistic experience in NeoMethaphisical Painting. Both the artist’s evolution trends and the process of shapes creation are emergent phenomena. Viewing the art in each period, accurate analysis allows us to identify the complexity of beauty and the perception of the harmony of created shapes, that are the signatures of the dynamical process of the artist in his creative efforts. The evolutionary trends of figurative arts further remark the fingerprints of complexity in the shape history. Moreover, if we try to establish when art arose, no definitive answer does exist. Art itself possibly arose before the birth of history. The examples of primitive art like the aboriginal cave paintings in Australia, representing hunt scenes, animals and even more abstract figures such as the half-human, half-animals figures called “therianthropes”, witness what