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

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.

The notion of structural coupling plays a central role in Maturana and Varela’s biology of cognition framework and strongly influenced Varela’s subsequent enactive elaboration of this framework. Building upon previous work using a glider in the Game of Life (GoL) cellular automaton as a toy model of a minimal autopoietic system with which to concretely explore these theoretical frameworks, this article presents an analysis of structural coupling between a glider and its environment. Specifically, for sufficiently small GoL universes, we completely characterize the nonautonomous dynamics of both a glider and its environment in terms of interaction graphs, derive the set of possible glider lives determined by the mutual constraints between these interaction graphs, and show how such lives are embedded in the state transition graph of the entire GoL universe.

Key words: autopoiesis, enaction, structural coupling, cellular automata, enactivism

Villalobos and Razeto-Barry’s target article highlights a debate about the role of spatial boundaries in autopoiesis that has been simmering for some time. I argue that, ultimately, controversies such as this are best resolved not by verbal argument, but rather in the context of actual mathematically formulated theories of biological individuality. Finally, I briefly review some initial efforts in this direction as they relate to the question of boundaries.

Key words: autopoiesis, boundary, toy model, theory, game of life.

Several authors have made claims about the compatibility between the Free Energy Principle (FEP) and theories of autopoiesis and enaction. Many see these theories as natural partners or as making similar statements about the nature of biological and cognitive systems. We critically examine these claims and identify a series of misreadings and misinterpretations of key enactive concepts. In particular, we notice a tendency to disregard the operational definition of autopoiesis and the distinction between a system’s structure and its organization. Other misreadings concern the conflation of processes of self-distinction in operationally closed systems with Markov blankets. Deeper theoretical tensions underlie some of these misinterpretations. FEP assumes systems that reach a non-equilibrium steady state and are enveloped by a Markov blanket. We argue that these assumptions contradict the historicity of agency and sense-making that is explicit in the enactive approach. Enactive concepts such as adaptivity and agency are defined in terms of the modulation of parameters and constraints of the agent-environment coupling, which entail the possibility of redefinition of variable and parameter sets and of the dynamical laws affecting a system, a situation that escapes the assumptions of FEP. In addition, the enactive perspective foregrounds the enabling and constitutive roles played by the world in sense-making, agency, development, and the path-dependent diversity of human bodies and minds. We argue that this position is also in contradiction with the FEP. Once we move beyond superficial similarities, identify misreadings, and examine the theoretical commitments of the two approaches, we reach the conclusion that the FEP, as it stands formulated today, is profoundly incompatible with the theories of autopoiesis and enaction.