A Model for Emergent Chaotic Order in Small Neural Networks

A new neural network model is introduced in this paper. The aim of the proposed Sierpinski neural networks is to provide a simple and biologically plausible neural network architecture that produces emergent complex spatio-temporal patterns through the activity of the output neurons of the network. Such networks can play an important role in the analysis and understanding of complex dynamic activity observed at various levels of biological neural systems. The proposed Sierpinski neural networks are described in detail and their functioning is analysed mathematicaly to show that they indeed produce Sierpinski triangles as the spatio-temporal activity patterns of their output neurons. The paper briefly discusses generalizations of the proposed neural networks, aspects of their biologically plausible realization, and their implication to the understanding of the role of biological neural chaos.