Spatiotemporal dynamics driven by the maximization of local information transfer

Abstract

In this paper, a generic type of a spatially extended system, which is driven by the maximization of information transfer in each spatiotemporal point, is proposed. As an expression of the information transfer, transfer entropy is addressed, and a one-dimensional cellular system (whose state transition is governed to maximize the local transfer entropy (LTE) from interacting cells) is introduced. We first show that this system’s mechanism of state transition can be considered equivalent to a certain class of cellular automata rules with memory. The spatiotemporal dynamics of the system is then investigated to generate a wide variety of patterns, including spatiotemporal intermittency, according to the length of memory. Furthermore, the spatiotemporal patterns of states and the resulting information dynamics are statistically characterized in detail, expressing the system’s diverse nature. In particular, it is found that, within a certain condition of limited memory, even if each cell is driven to maximize the LTE, the entire system cannot reach toward its theoretical maximum value at all due to its intrinsic property, in which the system is dynamically bounding its limit on its own.