We introduce a spatial model of concentration dynamics that supports the emergence of spatiotemporal inhomogeneities that engage in metabolism–boundary co-construction. These configurations exhibit disintegration following some perturbations, and self-repair in response to others. We define robustness as a viable configuration’s tendency to return to its prior configuration in response to perturbations, and plasticity as a viable configuration’s tendency to change to other viable configurations. These properties are demonstrated and quantified in the model, allowing us to map a space of viable configurations and their possible transitions. Combining robustness and plasticity provides a measure of viability as the average expected survival time under ongoing perturbation, and allows us to measure how viability is affected as the configuration undergoes transitions. The framework introduced here is independent of the specific model we used, and is applicable for quantifying robustness, plasticity, and viability in any computational model of artificial life that demonstrates the conditions for viability that we promote.

Key words: autopoiesis, viability, robustness, plasticity, spatial dynamical system, metabolism

Living agency is subject to a normative dimension (good-bad, adaptive-maladaptive) that is absent from other types of interaction. We review current and historical attempts to naturalize normativity from an organism-centered perspective, identifying two central problems and their solution: (1) How to define the topology of the viability space so as to include a sense of gradation that permits reversible failure, and (2) how to relate both the processes that establish norms and those that result in norm-following behavior. We present a minimal metabolic system that is coupled to a gradient-climbing chemotactic mechanism. Studying the relationship between metabolic dynamics and environmental resource conditions, we identify an emergent viable region and a precarious region where the system tends to die unless environmental conditions change. We introduce the concept of normative field as the change of environmental conditions required to bring the system back to its viable region. Norm-following, or normative action, is defined as the course of behavior whose effect is positively correlated with the normative field. We close with a discussion of the limitations and extensions of our model and some final reflections on the nature of norms and teleology in agency.

Maturana and Varela’s notion of autopoiesis has the potential to transform the conceptual foundation of biology as well as the cognitive, behavioral, and brain sciences. In order to fully realize this potential, however, the concept of autopoiesis and its many consequences require significant further theoretical and empirical development. A crucial step in this direction is the formulation and analysis of models of autopoietic systems. This article sketches the beginnings of such a project by examining a glider from Conway’s game of life in autopoietic terms. Such analyses can clarify some of the key ideas underlying autopoiesis and draw attention to some of the central open issues. This article also examines the relationship between an autopoietic perspective on cognition and recent work on dynamical approaches to the behavior and cognition of situated, embodied agents. Relevance: The article focuses on the theory of autopoiesis and related concepts such as structural coupling and cognitive domain.

This article examines in some technical detail the application of Maturana and Varela’s biology of cognition to a simple concrete model: a glider in the game of Life cellular automaton. By adopting an autopoietic perspective on a glider, the set of possible perturbations to it can be divided into destructive and nondestructive subsets. From a glider’s reaction to each nondestructive perturbation, its cognitive domain is then mapped. In addition, the structure of a glider’s possible knowledge of its immediate environment, and the way in which that knowledge is grounded in its constitution, are fully described. The notion of structural coupling is then explored by characterizing the paths of mutual perturbation that a glider and its environment can undergo. Finally, a simple example of a communicative interaction between two gliders is given. The article concludes with a discussion of the potential implications of this analysis for the enactive approach to cognition.

Key words: autopoiesis, enaction, cognitive domain, structural coupling, cellular automata.

Maturana and Varela’s concept of autopoiesis defines the essential organization of living systems and serves as a foundation for their biology of cognition and the enactive approach to cognitive science. As an initial step toward a more formal analysis of autopoiesis, this paper investigates its application to the compact, recurrent spatiotemporal patterns that arise in Conway’s Game of Life cellular automata. In particular, we demonstrate how such entities can be formulated as self-constructing networks of interdependent processes that maintain their own boundaries. We then characterize the specific organizations of several such entities, suggest a way to simplify the descriptions of these organizations, and briefly consider the transformation of such organizations over time. Relevance: The paper presents an analysis of a minimal concrete model of autopoiesis to provide a more rigorous foundation for the concept of autopoiesis and highlight its ambiguities and difficulties.

Using a glider in the Game of Life cellular automaton as a toy model, we explore how questions of origins might be approached from the perspective of autopoiesis. Specifically, we examine how the density of gliders evolves over time from random initial conditions and then develop a statistical mechanics of gliders that explains this time evolution in terms of the processes of glider creation, persistence and destruction that underlie it.

Enaction’s claim of continuity between life and mind is a bold one. We investigate one aspect of this claim using a glider in the Game of Life as a toy model. Specifically, we study the relationship between theories of glider constitution and glider interaction, demonstrating how a glider’s constitution completely determines its interaction graph, but not the particular life that it enacts, which also requires knowledge of the dynamics of its environment.

This article revisits the concept of autopoiesis and examines its relation to cognition and life. We present a mathematical model of a 3D tesselation automaton, considered as a minimal example of autopoiesis. This leads us to a thesis T1: “An autopoietic system can be described as a random dynamical system, which is defined only within its organized autopoietic domain.” We propose a modified definition of autopoiesis: “An autopoietic system is a network of processes that produces the components that reproduce the network, and that also regulates the boundary conditions necessary for its ongoing existence as a network.” We also propose a definition of cognition: “A system is cognitive if and only if sensory inputs serve to trigger actions in a specific way, so as to satisfy a viability constraint.” It follows from these definitions that the concepts of autopoiesis and cognition, although deeply related in their connection with the regulation of the boundary conditions of the system, are not immediately identical: a system can be autopoietic without being cognitive, and cognitive without being autopoietic. Finally, we propose a thesis T2: “A system that is both autopoietic and cognitive is a living system.”

Key words: Autopoiesis, cognition, life, tessela- tion automaton, random dynamical system, boundary conditions