CHAOTIC DYNAMICS OF LINGUISTIC-LIKE PROCESSES AT THE SYNTACTICAL AND SEMANTIC LEVELS: IN THE PURSUIT OF A MULTIFRACTAL ATTRACTOR

Collective parameters such as the Zipf's law-like statistics, the Transinformation, the Block Entropy and the Markovian character are compared for natural, genetic, musical and artificially generated long texts from generating partitions (alphabets) on homogeneous as well as on multifractal chaotic maps. It appears that minimal requirements for a language at the syntactical level such as memory, selectivity of few keywords and broken symmetry in one dimension (polarity) are more or less met by dynamically iterating simple maps or flows e.g. very simple chaotic hardware. The same selectivity is observed at the semantic level where the aim refers to partitioning a set of enviromental impinging stimuli onto coexisting attractors-categories. Under the regime of pattern recognition and classification, few key features of a pattern or few categories claim the lion's share of the information stored in this pattern and practically, only these key features are persistently scanned by the cognitive processor. A multifractal attractor model can in principle explain this high selectivity, both at the syntactical and the semantic levels.