This paper presents Coralai, a framework for exploring diverse ecosystems of Neural Cellular Automata (NCA). Organisms in Coralai utilize modular, GPU-accelerated Taichi kernels to interact, enact environmental changes, and evolve through local survival, merging, and mutation operations implemented with HyperNEAT and PyTorch. We provide an exploratory experiment implementing physics inspired by slime mold behavior showcasing the emergence of competition between sessile and mobile organisms, cycles of resource depletion and recovery, and symbiosis between diverse organisms. We conclude by outlining future work to discover simulation parameters through measures of multi-scale complexity and diversity. Code for Coralai is available at https://github.com/aidanbx/coralai , video demos are available at https://www.youtube.com/watch?v=NL8IZQY02-8 .

Evolution must explain both its ability to produce beneficial innovations as well as preserve organisms’ existing functional adaptedness to their environment. A proposed mechanism which resolves this tension is the concept of neutral networks, wherein mutations are not strictly beneficial or deleterious but neutral in their effect on organisms’ adaptedness. Neutral networks have been shown to be both prevalent and vast at multiple levels of biological organization. Additionally, there is much philosophical debate regarding how information flows between and across these levels of organization in reality. However, how to pragmatically engineer systems with multiscale structure to harness the inherent robustness that neutral networks confer remains largely unexplored. Here we show that, in hierarchical neural cellular automata (HNCA), various inter-scale connectivity architectures support mutational robustness and evolvability through the formation of neutral networks, wherein similar functional outcomes (e.g., morphogenesis, homeostasis) are achievable through diverse pathways of multiscale interactions. These findings can help inform the way we engineer artificial multiscale systems, e.g. hierarchical arrangements of robots. Operationalizing these insights may offer new ways of designing and engineering intelligent, robust, and adaptive machines. Additionally, the connection structures we explore have philsophical implications which may inform discussions of causal emergence in complex systems.

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.

Autopoiesis aims to describe the organization and limits of living systems. Unfortunately, its theoretical development has largely been carried out verbally, with less focus on developing formal concepts of the key ideas, such as structure, organization, process, etc. Using toy models of emergent individuals allows us to fully characterize these concepts concretely. This paper generalizes previous work that analysed autopoiesis in the Game of Life. I use the Larger than Life family of cellular automata to explore how the concepts of production process, autopoietic network, and cognitive domain extend to this space, before moving to the continuum limit in RealLife — a continuous-space, discrete-time family of Euclidean automata.

We introduce a minimal model of a thermodynamic agent capable of maintaining far-from-equilibrium states by actively harvesting and storing free energy from its environment. Inspired by minimal models of autonomy like Bittorio (Varela et al., 1991), our agent —labelled Thermina —gives shape to a theoretical framework for studying the interplay between thermodynamics and autonomy. By analytically studying the nonequilibrium steady state of the system, we distinguish between regions of ‘autonomous’ states —sustaining themselves out-of-equilibrium by harvesting free energy from the environment— and regions of ‘non-autonomous’ states —close to thermodynamic equilibrium and with very low chances of gathering free energy. Furthermore, we inspect the adaptive mechanisms that allow an agent to regulate its interaction with the environment to robustly maintain its nonequilibrium state. Studying in detail the behaviour of the system, we aim to provide insights into the broader question of how thermodynamic processes contribute to the emergence and maintenance of complex, adaptive behaviour in natural and artificial systems.

We introduce Biomaker CA: a Biome Maker project using Cellular Automata (CA). In Biomaker CA, morphogenesis is a first class citizen and small seeds need to grow into plantlike organisms to survive in a nutrient starved environment and eventually reproduce with variation so that a biome survives for long timelines. We simulate complex biomes by means of CA rules in 2D grids and parallelize all of its computation on GPUs through the Python JAX framework. We show how this project allows for several different kinds of environments and laws of ‘physics’, alongside different model architectures based on Neural Cellular Automata (NCA) and mutation strategies. We further analyze some configurations to show how plant agents can grow, survive, reproduce, and evolve, forming stable and unstable biomes. We then demonstrate how one can meta-evolve models to survive in a harsh environment either through end-to-end meta-evolution or by a more surgical and efficient approach, called Petri dish metaevolution. Finally, we show how to perform interactive evolution, where the user decides how to evolve a plant model interactively and then deploys it in a larger environment. We open source Biomaker CA at: https://tinyurl.com/2x8yu34s .

This study presents Dynamics Identification via Neural Cellular Automata (DINCA), an enhancement of Neural Cellular Automata (NCA) for modeling reaction-diffusion systems. The main advantage of DINCA is its ability to estimate the parameters of the reaction-diffusion equations that govern the examined system, using minimal data. We demonstrate the method’s application potential by showing its ability to model leopard pattern formation, by learning on only three images, while revealing the governing reaction-diffusion equations. This positions NCA-based methodologies as a viable tool for inferring partial differential equations. The code is available at https://github.com/koutefra/dinca .

Logic gates form the basis of modern digital computers, and from a theoretical perspective they are the unit of computation since they are the fundamental discrete logic element. By creating circuits of interconnected logic gates, computers can calculate more complex operations, such as adders, multiplexers, flips-flops, and eventually processing and control units. Herein, we use a 3D-printed platform consisting of a rectangular 2D-array of interconnected cells containing the Belousov–Zhabotinsky (BZ) reaction. This reaction can be made to oscillate between two states to simulate the binary codification of digital electronics. Within the platform each cell contains a magnetic stirrer that can be individually stirred to control the local oscillations of the BZ reaction in that cell, but all the cells are also weakly interconnected through the common medium, and here we used the convolution of their individual oscillations to perform heterotic computations. Moreover, the 3D-printed vessel can be fabricated using different architectures, to for example define how the cells are connected, and thus controlling how the oscillations propagate between them. We took advantage of these features to simulate the ”AND”, ”OR, and ”XOR” logic gates. We also implemented a 2D Cellular Automata. To do so we defined the cells where the BZ reaction oscillates as “on”, and set the transition rule as the propagation of oscillations from the “on” cells towards “off” ones. These results pave the way towards the development of more sophisticated unconventional computers, which might potentially enhance future Artificial Life implementations more effectively than current silicon-based advancements.