The idea that there is an edge of chaos , a region in the space of dynamical systems having special meaning for complex living entities, has a long history in artificial life. The significance of this region was first emphasized in cellular automata models when a single simple measure, λ CA , identified it as a transitional region between order and chaos. Here we introduce a parameter λ NN that is inspired by λ CA but is defined for recurrent neural networks. We show through a series of systematic computational experiments that λ NN generally orders the dynamical behaviors of randomly connected/weighted recurrent neural networks in the same way that λ CA does for cellular automata. By extending this ordering to larger values of λ NN than has typically been done with λ CA and cellular automata, we find that a second edge-of-chaos region exists on the opposite side of the chaotic region. These basic results are found to hold under different assumptions about network connectivity, but vary substantially in their details. The results show that the basic concept underlying the lambda parameter can usefully be extended to other types of complex dynamical systems than just cellular automata.

Cellular automata models have historically been a major approach to studying the information-processing properties of self-replication. Here we explore the feasibility of adopting genetic programming so that, when it is given a fairly arbitrary initial cellular automata configuration, it will automatically generate a set of rules that make the given configuration replicate. We found that this approach works surprisingly effectively for structures as large as 50 components or more. The replication mechanisms discovered by genetic programming work quite differently than those of many past manually designed replicators: There is no identifiable instruction sequence or construction arm, the replicating structures generally translate and rotate as they reproduce, and they divide via a fissionlike process that involves highly parallel operations. This makes replication very fast, and one cannot identify which descendant is the parent and which is the child. The ability to automatically generate self-replicating structures in this fashion allowed us to examine the resulting replicators as their properties were systematically varied. Further, it proved possible to produce replicators that simultaneously deposited secondary structures while replicating, as in some past manually designed models. We conclude that genetic programming is a powerful tool for studying self-replication that might also be profitably used in contexts other than cellular spaces.

Self-organizing particle systems consist of numerous autonomous, purely reflexive agents (“particles”) whose collective movements through space are determined primarily by local influences they exert upon one another. Inspired by biological phenomena (bird flocking, fish schooling, etc.), particle systems have been used not only for biological modeling, but also increasingly for applications requiring the simulation of collective movements such as computer-generated animation. In this research, we take some first steps in extending particle systems so that they not only move collectively, but also solve simple problems. This is done by giving the individual particles (agents) a rudimentary intelligence in the form of a very limited memory and a top-down, goal-directed control mechanism that, triggered by appropriate conditions, switches them between different behavioral states and thus different movement dynamics. Such enhanced particle systems are shown to be able to function effectively in performing simulated search-and-collect tasks. Further, computational experiments show that collectively moving agent teams are more effective than similar but independently moving ones in carrying out such tasks, and that agent teams of either type that split off members of the collective to protect previously acquired resources are most effective. This work shows that the reflexive agents of contemporary particle systems can readily be extended to support goal-directed problem solving while retaining their collective movement behaviors. These results may prove useful not only for future modeling of animal behavior, but also in computer animation, coordinated movement control in robotic teams, particle swarm optimization, and computer games.

In a number of multi-agent artificial life studies where agents interact over limited distances, the emergence and/or evolution of a specific behavior may depend critically upon interagent distances. Little theoretical analysis has been done previously concerning how to predict such distances. In this paper, we derive a probabilistic method that, for an agent at an arbitrary location in a two-dimensional cellular world, predicts the expected distance to a nearest other agent. Our method works for many world topologies, and we apply it to determine the expected distance for six commonly used ones. Further, the method is readily adapted to handle special restrictions. Over a wide variety of agent densities we show that the theoretically predicted distances are largely in agreement with the distances measured in computational experiments with randomly placed agents. We then utilize our prediction method to interpret recent observations that an imprecise threshold in the density of agents exists for the evolution of communication. We thus illustrate that, despite its conceptual simplicity, our method can aid the analysis and even the design of complex artificial environments populated by agents that have the potential to interact with one another.

In the research described here we extend past computational investigations of animal signaling by studying an artificial world in which a population of initially noncommunicating agents evolves to communicate about food sources and predators. Signaling in this world can be either beneficial (e.g., warning of nearby predators) or costly (e.g., attracting predators or competing agents). Our goals were twofold: to examine systematically environmental conditions under which grounded signaling does or does not evolve, and to determine how variations in assumptions made about the evolutionary process influence the outcome. Among other things, we found that agents warning of nearby predators were a common occurrence whenever predators had a significant impact on survival and signaling could interfere with predator success. The setting most likely to lead to food signaling was found to be difficult-to-locate food sources that each have relatively large amounts of food. Deviations from the selection methods typically used in traditional genetic algorithms were also found to have a substantial impact on whether communication evolved. For example, constraining parent selection and child placement to physically neighboring areas facilitated evolution of signaling in general, whereas basing parent selection upon survival alone rather than survival plus fitness measured as success in food acquisition was more conducive to the emergence of predator alarm signals. We examine the mechanisms underlying these and other results, relate them to existing experimental data about animal signaling, and discuss their implications for artificial life research involving evolution of communication.

Since von Neumann's seminal work around 1950, computer scientists and others have studied the algorithms needed to support self-replicating systems. Much of this work has focused on abstract logical machines (automata) embedded in two-dimensional cellular spaces. This research was motivated by the desire to understand the basic information-processing principles underlying self-replication, the potential long-term applications of programmable self-replicating machines, and the possibility of gaining insight into biological replication and the origins of life. We view past research as taking three main directions: early complex universal computer-constructors modeled after Turing machines, qualitatively simpler self-replicating loops, and efforts to view self-replication as an emergent phenomenon. We discuss our recent studies in the latter category showing that self-replicating structures can emerge from nonreplicating components, and that genetic algorithms can be applied to program automatically simple but arbitrary structures to replicate. We also describe recent work in which self-replicating structures are successfully programmed to do useful problem solving as they replicate. We conclude by identifying some implications and important research directions for the future.

There have been various attempts to simulate the self-assembly process of lipid aggregates by computers. However, due to the computationally complex nature of the problem, previous simulations were often conducted with unrealistic simplifications of the molecules' morphology, intermolecular interactions, and the environment in which the lipid molecules interact. In this article, we present a new computational model in which each lipid is simulated by a more realistic amphiphilic particle consisting of a hydrophilic head and a long hydrophobic tail. The intermolecular interactions are approximated by a set of simple forces reflecting physical and chemical properties of lipids, for example, hydrophobicity and electrostatic forces, which are believed to be crucial for the formation of various aggregates. With a set of carefully selected parameters, this model is able to simulate successfully the formation of micelles in an aqueous environment and reversed micelle structures in an oil solvent from an initially randomly distributed set of lipidlike particles. This model can be used to study, at the microscopic level, the self-assembly of different protocell structures in the evolutionary process and the impact of environmental conditions on the formation of these structures. It may be further generalized to simulate the formation of other, more complex structures of amphiphilic molecules such as monolayer and bilayer aggregates.