Local measures of information storage in complex distributed computation

Abstract

Information storage is a key component of intrinsic distributed computation. Despite the existence of appropriate measures for it (e.g. excess entropy), its role in interacting with information transfer and modification to give rise to distributed computation is not yet well-established. We explore how to quantify information storage on a local scale in space and time, so as to understand its role in the dynamics of distributed computation. To assist these explorations, we introduce the active information storage, which quantifies the information storage component that is directly in use in the computation of the next state of a process. We present the first profiles of local excess entropy and local active information storage in cellular automata, providing evidence that blinkers and background domains are dominant information storage processes in these systems. This application also demonstrates the manner in which these two measures of information storage are distinct but complementary. It also reveals other information storage phenomena, including the misinformative nature of local storage when information transfer dominates the computation, and demonstrates that the local entropy rate is a useful spatiotemporal filter for information transfer structure.