Biological systems exhibit hierarchical and intricate mechanisms that enable self-sustenance and open-ended behavior. This organizational closure is arguably one of life’s hallmarks, and it is facilitated by the widespread utilization of enzymes. Enzymes enhance improbable pathways, enabling the formation of complex structures and functions. Here, we propose a model to characterize artificial enzymes within an artificial “soup” of functions. We contend that these enzymes can emerge from elementary interactions among functions, and they should foster rapid complexity growth, owing to their ability to construct auto-catalitic networks.

An explanatory model for the emergence of evolvable units must display emerging structures that (1) preserve themselves in time (2) self-reproduce and (3) tolerate a certain amount of variation when reproducing. To tackle this challenge, here we introduce Combinatory Chemistry, an Algorithmic Artificial Chemistry based on a minimalistic computational paradigm named Combinatory Logic. The dynamics of this system comprise very few rules, it is initialized with an elementary tabula rasa state, and features conservation laws replicating natural resource constraints. Our experiments show that a single run of this dynamical system with no external intervention discovers a wide range of emergent patterns. All these structures rely on acquiring basic constituents from the environment and decomposing them in a process that is remarkably similar to biological metabolisms. These patterns include autopoietic structures that maintain their organisation, recursive ones that grow in linear chains or binary-branching trees, and most notably, patterns able to reproduce themselves, duplicating their number at each generation.

Complex systems can exhibit autopoiesis–a remarkable capability to reproduce or restore themselves to maintain existence and functionality. We explore the resilience of autopoietic patterns–their ability to recover from shocks or perturbations–in a simplified form in Conway's Game of Life. We subject a large number of autopoietic patterns in the Game of Life to various perturbations, and record their responses using multiple resilience metrics. Our results show that while resilience is rare, we are able to identify structural features improving patterns' resilience. We also draw several parallels between the resilience of patterns in the Game of Life to real-world complex systems. Our work may be useful both for improved searching for resilient patterns in the Game of Life, and for exploring resilience in complex systems.