1 Introduction
Distributed dynamical systems like cellular automata (CAs) and random boolean networks (RBNs) (and everything in between) have long been used as models to understand computation and self-replication in biology, morphogenesis, gene regulation, life-as-it-could-be, and the Universe.
Such complex system models have been extensively studied mathematically and experimentally in all their different variations, such as synchronous and asynchronous updates and dynamic automata networks that can grow and change their structure, including components and interconnection topology, as well as their robustness.
Wuensche (1994) investigated the basins of attraction of CAs and RBNs and even suggested that they are the “ghost in the machine.”
Recent advances in such models, including continuous CAs, such as Lenia (Chan, 2019), and neural-based CAs (Mordvintsev et al., 2020), have been proposed as substrates to study the emergence of a more general intelligence (Gregor & Besse, 2021; Hamon et al., 2022), thanks to their propensity to support properties like self-organization, emergence, and open-endedness.
But what can we learn from CAs and distributed dynamical system models about intelligence? And how can CAs and distributed dynamical system models be used to study the emergence of intelligence?
To address such questions, we organized a workshop at the 2023 Artificial Life conference in Sapporo, Japan, that aimed to bridge the gap between the ALife community working with CAs and distributed dynamical systems and the broader artificial intelligence (AI) community interested in exploring concepts from complex systems, self-organization, and Artificial Life for AI research and machine learning.
The workshop was named “The Distributed Ghost,” inspired by the Artificial Life conference theme “Ghost in the Machine.” The workshop program (Nichele et al., 2023) consisted of two invited keynotes, by Bert Chan and Andrea Roli, and a set of 10 abstract-based presentations. After the workshop, four high-quality contributions were extended as full papers and have been collected in this special issue.
In “Cell-Cell Interactions: How Coupled Boolean Networks Tend to Criticality,” Braccini and coauthors investigate interacting RBNs as a theoretical model of multicellular biological systems with cell–cell interactions. They find not only that the interacting versions of RBNs show the same general trends of dynamical properties as their individual counterparts but also that the networks in ordered or chaotic regimes tend toward a critical regime when turned into interacting networks (while individually critical networks remain critical). This result suggests the importance of the interconnected nature of a distributed multicellular system for its system-level criticality (and thus biological functioning) as a whole.
In “Emergence of Self-Replicating Hierarchical Structures in a Binary Cellular Automaton,” using genetic programming to explore the vast space of binary CAs (with Moore neighborhood and rotationally symmetric rule sets in two dimensions) for open-ended temporal evolution, Yang reports on the discovery of a novel CA rule, the “Outlier.” Most strikingly, this CA and therefore also its distinct chiral twin (obtained by mirroring the rule table) are unique among known models of self-replication in that structures exhibit replication across two different nested spatiotemporal scales. Moreover, the self-replicating structures appear from sparse random initial conditions and follow characteristic attractor trajectories involving such multiscale self-replication.
In “Survival and Evolutionary Adaptation of Populations Under Disruptive Habitat Change: A Study With Darwinian Cellular Automata,” Derets and Nehaniv focus on the evolution of living beings, emphasizing continuous adaptation akin to Darwinian principles within the domain of Artificial Life. The introduced model addresses the survival of organisms amid environmental changes, particularly during transitions to less favorable conditions (modeled using percolation theory). A probabilistic CA is employed based on update rules derived from genetic algorithm principles. Finally, an experimental investigation of the model’s behavioral features is presented, analyzing parameters and thresholds governing population survival or extinction outcomes.
In “Self-Reproduction and Evolution in Cellular Automata: 25 Years After Evoloops,” Sayama and Nehaniv offer a comprehensive review of advancements in CAs subjected to Darwinian evolution. The contribution marks the 25th anniversary of the seminal work on evoloops (Sayama, 1999). The review highlights significant developments, ongoing challenges, and prospective research avenues in Artificial Life, focusing on self-reproducing and evolving patterns in distributed computational environments.
We are continuing the tradition of the “distributed series” in 2024 by organizing a special session named “The Distributed Viking” at the Artificial Life conference in Copenhagen, Denmark. More information can be found at the special session web page (https://www.nichele.eu/ALIFE-DistributedViking/).