The year 2024 marks the 25th anniversary of the publication of evoloops, an evolutionary variant of Chris Langton’s self-reproducing loops, which proved constructively that Darwinian evolution of self-reproducing organisms by variation and natural selection is possible within deterministic cellular automata. Over the last few decades, this line of Artificial Life research has since undergone several important developments. Although it experienced a relative dormancy of activity for a while, the recent rise of interest in open-ended evolution and the success of continuous cellular automata models have brought researchers’ attention back to how to make spatiotemporal patterns self-reproduce and evolve within spatially distributed computational media. This article provides a review of the relevant literature on this topic over the past 25 years and highlights the major accomplishments made so far, the challenges being faced, and promising future research directions.

Cooperation among individuals has been key to sustaining societies. However, natural selection favors defection over cooperation. Cooperation can be favored when the mobility of individuals allows cooperators to form a cluster (or group). Mobility patterns of animals sometimes follow a Lévy flight. A Lévy flight is a kind of random walk but it is composed of many small movements with a few big movements. The role of Lévy flights for cooperation has been studied by Antonioni and Tomassini, who showed that Lévy flights promoted cooperation combined with conditional movements triggered by neighboring defectors. However, the optimal condition for neighboring defectors and how the condition changes with the intensity of Lévy flights are still unclear. Here, we developed an agent-based model in a square lattice where agents perform Lévy flights depending on the fraction of neighboring defectors. We systematically studied the relationships among three factors for cooperation: sensitivity to defectors, the intensity of Lévy flights, and population density. Results of evolutionary simulations showed that moderate sensitivity most promoted cooperation. Then, we found that the shortest movements were best for cooperation when the sensitivity to defectors was high. In contrast, when the sensitivity was low, longer movements were best for cooperation. Thus, Lévy flights, the balance between short and long jumps, promoted cooperation in any sensitivity, which was confirmed by evolutionary simulations. Finally, as the population density became larger, higher sensitivity was more beneficial for cooperation to evolve. Our study highlights that Lévy flights are an optimal searching strategy not only for foraging but also for constructing cooperative relationships with others.

Cellular automata (CA) have been lauded for their ability to generate complex global patterns from simple local rules. The late English mathematician, John Horton Conway, developed his illustrious Game of Life (Life) CA in 1970, which has since remained one of the most quintessential CA constructions—capable of producing a myriad of complex dynamic patterns and computational universality. Life and several other Life-like rules have been classified in the same group of aesthetically and dynamically interesting CA rules characterized by their complex behaviors. However, a rigorous quantitative comparison among similarly classified Life-like rules has not yet been fully established. Here we show that Life is capable of maintaining as much complexity as similar rules while remaining the most parsimonious. In other words, Life contains a consistent amount of complexity throughout its evolution, with the least number of rule conditions compared to other Life-like rules. We also found that the complexity of higher density Life-like rules, which themselves contain the Life rule as a subset, form a distinct concave density-complexity relationship whereby an optimal complexity candidate is proposed. Our results also support the notion that Life functions as the basic ingredient for cultivating the balance between structure and randomness to maintain complexity in 2D CA for low- and high-density regimes, especially over many iterations. This work highlights the genius of John Horton Conway and serves as a testament to his timeless marvel, which is referred to simply as: Life.

The El Farol Bar problem highlights the issue of bounded rationality through a coordination problem where agents must decide individually whether or not to attend a bar without prior communication. Each agent is provided a set of attendance predictors (or decision-making strategies) and uses the previous bar attendances to guess bar attendance for a given week to determine if the bar is worth attending. We previously showed how the distribution of used strategies among the population settles into an attractor by using a spatial phase space. However, this approach was limited as it required N − 1 dimensions to fully visualize the phase space of the problem, where N is the number of strategies available. Here we propose a new approach to phase space visualization and analysis by converting the strategy dynamics into a state transition network centered on strategy distributions. The resulting weighted, directed network gives a clearer representation of the strategy dynamics once we define an attractor of the strategy phase space as a sink-strongly connected component. This enables us to study the resulting network to draw conclusions about the performance of the different strategies. We find that this approach not only is applicable to the El Farol Bar problem, but also addresses the dimensionality issue and is theoretically applicable to a wide variety of discretized complex systems.

Self-organization can be broadly defined as the ability of a system to display ordered spatiotemporal patterns solely as the result of the interactions among the system components. Processes of this kind characterize both living and artificial systems, making self-organization a concept that is at the basis of several disciplines, from physics to biology and engineering. Placed at the frontiers between disciplines, artificial life (ALife) has heavily borrowed concepts and tools from the study of self-organization, providing mechanistic interpretations of lifelike phenomena as well as useful constructivist approaches to artificial system design. Despite its broad usage within ALife, the concept of self-organization has been often excessively stretched or misinterpreted, calling for a clarification that could help with tracing the borders between what can and cannot be considered self-organization. In this review, we discuss the fundamental aspects of self-organization and list the main usages within three primary ALife domains, namely “soft” (mathematical/computational modeling), “hard” (physical robots), and “wet” (chemical/biological systems) ALife. We also provide a classification to locate this research. Finally, we discuss the usefulness of self-organization and related concepts within ALife studies, point to perspectives and challenges for future research, and list open questions. We hope that this work will motivate discussions related to self-organization in ALife and related fields.

Open-ended evolution requires unbounded possibilities that evolving entities can explore. The cardinality of a set of those possibilities thus has a significant implication for the open-endedness of evolution. I propose that facilitating formation of higher-order entities is a generalizable, effective way to cause a cardinality leap in the set of possibilities that promotes open-endedness. I demonstrate this idea with a simple, proof-of-concept toy model called Hash Chemistry that uses a hash function as a fitness evaluator of evolving entities of any size or order. Simulation results showed that the cumulative number of unique replicating entities that appeared in evolution increased almost linearly along time without an apparent bound, demonstrating the effectiveness of the proposed cardinality leap. It was also observed that the number of individual entities involved in a single replication event gradually increased over time, indicating evolutionary appearance of higher-order entities. Moreover, these behaviors were not observed in control experiments in which fitness evaluators were replaced by random number generators. This strongly suggests that the dynamics observed in Hash Chemistry were indeed evolutionary behaviors driven by selection and adaptation taking place at multiple scales.

Open-endedness is often considered a prerequisite property of the whole evolutionary system and its dynamical behaviors. In the actual history of evolution on Earth, however, there are many examples showing that open-endedness is rather a consequence of evolution. We suggest that this view, which we call evolved open-endedness (EOE), be incorporated more into research on open-ended evolution. This view should allow for systematic investigation of more nuanced, more concrete research questions about open-endedness and its relationship with adaptation and sustainability.

Whereas the relationship between criticality of gene regulatory networks (GRNs) and dynamics of GRNs at a single-cell level has been vigorously studied, the relationship between the criticality of GRNs and system properties at a higher level has not been fully explored. Here we aim at revealing a potential role of criticality of GRNs in morphogenesis, which is hard to uncover through the single-cell-level studies, especially from an evolutionary viewpoint. Our model simulated the growth of a cell population from a single seed cell. All the cells were assumed to have identical intracellular GRNs. We induced genetic perturbations to the GRN of the seed cell by adding, deleting, or switching a regulatory link between a pair of genes. From numerical simulations, we found that the criticality of GRNs facilitated the formation of nontrivial morphologies when the GRNs were critical in the presence of the evolutionary perturbations. Moreover, the criticality of GRNs produced topologically homogeneous cell clusters by adjusting the spatial arrangements of cells, which led to the formation of nontrivial morphogenetic patterns. Our findings correspond to an epigenetic viewpoint that heterogeneous and complex features emerge from homogeneous and less complex components through the interactions among them. Thus, our results imply that highly structured tissues or organs in morphogenesis of multicellular organisms might stem from the criticality of GRNs.

It is well known that cooperation cannot be an evolutionarily stable strategy for a non-iterative game in a well-mixed population. In contrast, structured populations favor cooperation, since cooperators can benefit each other by forming local clusters. Previous studies have shown that scale-free networks strongly promote cooperation. However, little is known about the invasion mechanism of cooperation in scale-free networks. To study microscopic and macroscopic behaviors of cooperators' invasion, we conducted computational experiments on the evolution of cooperation in scale-free networks where, starting from all defectors, cooperators can spontaneously emerge by mutation. Since the evolutionary dynamics are influenced by the definition of fitness, we tested two commonly adopted fitness functions: accumulated payoff and average payoff. Simulation results show that cooperation is strongly enhanced with the accumulated payoff fitness compared to the average payoff fitness. However, the difference between the two functions decreases as the average degree increases. As the average degree increases, cooperation decreases for the accumulated payoff fitness, while it increases for the average payoff fitness. Moreover, for the average payoff fitness, low-degree nodes play a more important role in spreading cooperative strategies than for the accumulated payoff fitness.

We report a summary of our interdisciplinary research project “Evolutionary Perspective on Collective Decision Making” that was conducted through close collaboration between computational, organizational, and social scientists at Binghamton University. We redefined collective human decision making and creativity as evolution of ecologies of ideas, where populations of ideas evolve via continual applications of evolutionary operators such as reproduction, recombination, mutation, selection, and migration of ideas, each conducted by participating humans. Based on this evolutionary perspective, we generated hypotheses about collective human decision making, using agent-based computer simulations. The hypotheses were then tested through several experiments with real human subjects. Throughout this project, we utilized evolutionary computation (EC) in non-traditional ways—(1) as a theoretical framework for reinterpreting the dynamics of idea generation and selection, (2) as a computational simulation model of collective human decision-making processes, and (3) as a research tool for collecting high-resolution experimental data on actual collaborative design and decision making from human subjects. We believe our work demonstrates untapped potential of EC for interdisciplinary research involving human and social dynamics.

This letter presents a new, artificial-life-based view of the Collatz problem, a well-known mathematical problem about the behavior of a series of positive integers generated by a simple arithmetical rule. The Collatz conjecture asserts that this series always falls into a 4 → 2 → 1 cycle regardless of its initial values. No formal proof has been given yet. In this letter, the behavior of the series is considered an ecological process of artificial organisms (1s in bit strings). The Collatz conjecture is then reinterpreted as the competition between population growth and extinction. This new interpretation has made it possible to analytically calculate the growth and extinction speeds of bit strings. The results indicate that the extinction is always faster than the growth, providing an ecological explanation for the conjecture. Future research directions are also suggested.

We propose swarm chemistry , a new artificial chemistry framework that uses artificial swarm populations as chemical reactants. Reaction in swarm chemistry is not determined by predefined reaction rules as commonly assumed in typical artificial chemistry studies, but is spontaneously achieved by the emergence of a new spatiotemporal pattern of collective behavior through the kinetic interaction between multiple chemical species. We developed a prototype of an interactive simulation tool with which one can explore the dynamics of swarm chemistry using an interactive evolutionary method. Several preliminary results are reported to illustrate the characteristics and effectiveness of this framework, including spontaneous segregation of distinct chemical species, production and restriction of movements, and interactive design of complex biological-looking structures.

We present a general approach for evaluating and visualizing evolutionary dynamics of self-replicators using a graph-based representation for genealogy. Through a transformation from the space of species and mutations to the space of nodes and links, evolutionary dynamics are understood as a flow in graph space. A formalism is introduced to quantify such genealogical flows in terms of the complete history of localized evolutionary events recorded at the finest level of detail. Represented in a multidimensional viewing space, collective dynamical properties of an evolving genealogy are characterized in the form of aggregate flows. We demonstrate the effectiveness of this approach by using it to compare the evolutionary exploration behavior of self-replicating loops under two different environmental settings.

The concept of self-protection , a capability of an organism to protect itself from exogenous attacks, is introduced into the design of artificial evolutionary systems as a possible method to create and maintain diversity in the population. Three different mechanisms of self-protection are considered and implemented on a cellular-automaton-based evolutionary system, the evoloop . Simulation results imply a positive effect of those mechanisms on diversity maintenance, especially when the self-protection is moderate so that it conserves both the attacker and the attacked. This letter briefly reports the models and the simulation results obtained using those models.

We constructed a simple evolutionary system, “evoloop,” on a deterministic nine-state five-neighbor cellular automata (CA) space by improving the structurally dissolvable self-reproducing loop we had previously contrived [14] after Langton's self-reproducing loop [7]. The principal role of this improvement is to enhance the adaptability (a degree of the variety of situations in which structures in the CA space can operate regularly) of the self-reproductive mechanism of loops. The experiment with evoloop met with the intriguing result that, though no mechanism was explicitly provided to promote evolution, the loops varied through direct interaction of their phenotypes, smaller individuals were naturally selected thanks to their quicker self-reproductive ability, and the whole population gradually evolved toward the smallest ones. This result gives a unique example of evolution of self-replicators where genotypical variation is caused by precedent phenotypical variation. Such interrelation of genotype and phenotype would be one of the important factors driving the evolutionary process of primitive life forms that might have actually occurred in ancient times.