Elementary cellular automata deterministically map a binary sequence to another using simple local rules. Visualizing the structure of this mapping is difficult because the number of nodes (i.e. possible binary sequences) grows exponentially. If periodic boundary conditions are used, rotation of a sequence and rule application to that sequence commute. This allows us to recover the rotational invariance property of loops and to reduce the number of nodes by only considering binary necklaces , the equivalence class of n-character strings taking all rotations as equivalent. Combining together many equivalent histories reveals the general structure of the rule, both visually and computationally. In this work, we investigate the structure of necklace-networks induced by the 256 Elementary Cellular Automata rules and show how their network structure change as the length of necklaces grow.

Automatically identifying the stepping-stones that will lead to a predetermined final solution presents a significant challenge for optimization algorithms, yet is essential for solving complex problems. This study, inspired by Picbreeder, investigates a variation of NeuroEvolution of Augmenting Topologies (NEAT) which aims to perform an image replication task using Compositional Pattern Producing Networks (CPPNs) without a human in the loop. This challenge is central to many similar problems in evolutionary computation and artificial life, where identifying key intermediate goals known as stepping-stones is crucial but difficult, often requiring precise fine-tuning of solutions. We leverage techniques from deep learning computer vision research: a fitness function based on perceptual-similarity to help avoid deceptive optima, Fourier features to diversify the CPPNs’ inputs, and gradient-based backpropagation to balance the exploration of evolutionary search with goal-directed exploitation. Back-propagation has the additional benefit of smoothing the fitness landscape of topological network mutations. Our results indicate that combining these approaches with CPPN-NEAT yields more diverse and higher fitness solutions compared to traditional NEAT. This hybrid method not only preserves diversity, but also leverages the strengths of both evolutionary algorithms and gradient descent to achieve more detailed and accurate image generation. We speculate that this is a promising avenue for algorithm design, where exploiting gradient information can be balanced with maintaining robust diversity in the search process.

Catastrophic forgetting continues to severely restrict the learnability of controllers suitable for multiple task environments. Efforts to combat catastrophic forgetting reported in the literature to date have focused on how control systems can be updated more rapidly, hastening their adjustment from good initial settings to new environments, or more circumspectly, suppressing their ability to overfit to any one environment. When using robots, the environment includes the robot's own body, its shape and material properties, and how its actuators and sensors are distributed along its mechanical structure. Here we demonstrate for the first time how one such design decision (sensor placement) can alter the landscape of the loss function itself, either expanding or shrinking the weight manifolds containing suitable controllers for each individual task, thus increasing or decreasing their probability of overlap across tasks, and thus reducing or inducing the potential for catastrophic forgetting.

Because the kind of open-ended complexity explosion seen on Earth remains beyond the observed dynamics of current artificial life worlds, it has become critical to isolate and investigate specific factors that may contribute to open-endedness. This paper focuses on one such factor that has previously received little attention in research on open-endedness: the minimal criterion (MC) for reproduction. Originally proposed as an enhancement to novelty search, the MC is in effect a different abstraction of evolution than the more conventional competition-focused fitness-based paradigm, instead focusing on the minimal task that must be completed for an organism to be allowed to produce offspring. The MC is interesting for studying open-endedness because in principle its strictness (i.e. how hard it is to satisfy) can be varied on a continuum to observe its effects. While in many artificial life worlds the MC strictness is implicit and therefore difficult to vary systematically, in the previously-introduced Chromaria world, the MC is designed to be set explicitly by the experimenter, making possible the systematic study of different levels of MC strictness in this paper. The main result, supported by visual, quantitative, and qualitative observations, is that the strictness of the MC can profoundly affect open- ended dynamics, ultimately deciding between complete stagnation (both with extreme strictness or complete relaxation) and orderly divergence. This result offers a lesson of particular importance to worlds whose MCs are not explicit by exposing an area of sensitivity within open-ended systems that is easy to overlook because of its implicit nature.

The concept of morphological computation holds that the body of an agent can, under certain circumstances, exploit the interaction with the environment to achieve useful behavior, potentially reducing the computational burden of the brain/controller. The conditions under which such phenomenon arises are, however, unclear. We hypothesize that morphological computation will be facilitated by body plans with appropriate geometric, material, and growth properties, while it will be hindered by other body plans in which one or more of these three properties is not well suited to the task. We test this by evolving the geometries and growth processes of soft robots, with either manually-set softer or stiffer material properties. Results support our hypothesis: we find that for the task investigated, evolved softer robots achieve better performances with simpler growth processes than evolved stiffer ones. We hold that the softer robots succeed because they are better able to exploit morphological computation. This four-way interaction among geometry, growth, material properties and morphological computation is but one example phenomenon that can be investigated using the system here introduced, that could enable future studies on the evolution and development of generic soft-bodied creatures.