Biological systems exhibit remarkable morphogenetic plasticity, where a single genome can encode various specialized cellular structures triggered by local chemical signals. In the domain of Deep Learning, Differentiable Neural Cellular Automata (NCA) have emerged as a paradigm to mimic this self-organization. However, existing NCA research has predominantly focused on continuous texture synthesis or single-target object recovery, leaving the challenge of class-conditional structural generation largely unexplored. In this work, we propose a novel Conditional Neural Cellular Automata (c-NCA) architecture capable of growing distinct topological structures - specifically MNIST digits - from a single generic seed, guided solely by a spatially broadcasted class vector. Unlike traditional generative models (e.g., GANs, VAEs) that rely on global reception fields, our model enforces strict locality and translation equivariance. We demonstrate that by injecting a one-hot condition into the cellular perception field, a single set of local rules can learn to break symmetry and self-assemble into ten distinct geometric attractors. Experimental results show that our c-NCA achieves stable convergence, correctly forming digit topologies from a single pixel, and exhibits robustness characteristic of biological systems. This work bridges the gap between texture-based NCAs and structural pattern formation, offering a lightweight, biologically plausible alternative for conditional generation.

Cellular automata and their differentiable counterparts, Neural Cellular Automata (NCA), are highly expressive and capable of surprisingly complex behaviors. This paper explores how NCAs perform when applied to tasks requiring precise transformations and few-shot generalization, using the Abstraction and Reasoning Corpus for Artificial General Intelligence (ARC-AGI) as a domain that challenges their capabilities in ways not previously explored. Specifically, this paper uses gradient-based training to learn iterative update rules that transform input grids into their outputs from the training examples and then applies them to the test inputs. Results suggest that gradient-trained NCA models are a promising and efficient approach to a range of abstract grid-based tasks from ARC. Along with discussing the impacts of various design modifications and training constraints, this work examines the behavior and properties of NCAs applied to ARC to give insights for broader applications of self-organizing systems.

Neural Cellular Automata (NCA) represent a powerful framework for modeling biological self-organization, extending classical rule-based systems with trainable, differentiable (or evolvable) update rules that capture the adaptive self-regulatory dynamics of living matter. By embedding Artificial Neural Networks (ANNs) as local decision-making centers and interaction rules between localized agents, NCA can simulate processes across molecular, cellular, tissue, and system-level scales, offering a multiscale competency architecture perspective on evolution, development, regeneration, aging, morphogenesis, and robotic control. These models not only reproduce biologically inspired target patterns but also generalize to novel conditions, demonstrating robustness to perturbations and the capacity for open-ended adaptation and reasoning. Given their immense success in recent developments, we here review current literature of NCAs that are relevant primarily for biological or bioengineering applications. Moreover, we emphasize that beyond biology, NCAs display robust and generalizing goal-directed dynamics without centralized control, e.g., in controlling or regenerating composite robotic morphologies or even on cutting-edge reasoning tasks such as ARC-AGI-1. In addition, the same principles of iterative state-refinement is reminiscent to modern generative Artificial Intelligence (AI), such as probabilistic diffusion models. Their governing self-regulatory behavior is constraint to fully localized interactions, yet their collective behavior scales into coordinated system-level outcomes. We thus argue that NCAs constitute a unifying computationally lean paradigm that not only bridges fundamental insights from multiscale biology with modern generative AI, but have the potential to design truly bio-inspired collective intelligence capable of hierarchical reasoning and control.

Brain morphology is shaped by genetic and mechanical factors and is linked to biological development and diseases. Its fractal-like features, regional anisotropy, and complex curvature distributions hinder quantitative insights in medical inspections. Recognizing that the underlying elastic instability and bifurcation share the same physics as simple geometries such as spheres and ellipses, we developed a physics-transfer learning framework to address the geometrical complexity. To overcome the challenge of data scarcity, we constructed a digital library of high-fidelity continuum mechanics modeling that both describes and predicts the developmental processes of brain growth and disease. The physics of nonlinear elasticity from simple geometries is embedded into a neural network and applied to brain models. This physics-transfer approach demonstrates remarkable performance in feature characterization and morphogenesis prediction, highlighting the pivotal role of localized deformation in dominating over the background geometry. The data-driven framework also provides a library of reduced-dimensional evolutionary representations that capture the essential physics of the highly folded cerebral cortex. Validation through medical images and domain expertise underscores the deployment of digital-twin technology in comprehending the morphological complexity of the brain.

Neural Cellular Automata (NCAs) are a promising new approach to model self-organizing processes, with potential applications in life science. However, their deterministic nature limits their ability to capture the stochasticity of real-world biological and physical systems. We propose the Mixture of Neural Cellular Automata (MNCA), a novel framework incorporating the idea of mixture models into the NCA paradigm. By combining probabilistic rule assignments with intrinsic noise, MNCAs can model diverse local behaviors and reproduce the stochastic dynamics observed in biological processes. We evaluate the effectiveness of MNCAs in three key domains: (1) synthetic simulations of tissue growth and differentiation, (2) image morphogenesis robustness, and (3) microscopy image segmentation. Results show that MNCAs achieve superior robustness to perturbations, better recapitulate real biological growth patterns, and provide interpretable rule segmentation. These findings position MNCAs as a promising tool for modeling stochastic dynamical systems and studying self-growth processes.

Understanding and manipulating bioelectric signaling could present a new wave of progress in developmental biology, regenerative medicine, and synthetic biology. Bioelectric signals, defined as voltage gradients across cell membranes caused by ionic movements, play a role in regulating crucial processes including cellular differentiation, proliferation, apoptosis, and tissue morphogenesis. Recent studies demonstrate the ability to modulate these signals to achieve controlled tissue regeneration and morphological outcomes in organisms such as planaria and frogs. However, significant knowledge gaps remain, particularly in predicting and controlling the spatial and temporal dynamics of membrane potentials (V_mem), understanding their regulatory roles in tissue and organ development, and exploring their therapeutic potential in diseases. In this work we propose an experiment using Deep Reinforcement Learning (DRL) framework together with lab automation techniques for real-time manipulation of bioelectric signals to guide tissue regeneration and morphogenesis. The proposed framework should interact continuously with biological systems, adapting strategies based on direct biological feedback. Combining DRL with real-time measurement techniques -- such as optogenetics, voltage-sensitive dyes, fluorescent reporters, and advanced microscopy -- could provide a comprehensive platform for precise bioelectric control, leading to improved understanding of bioelectric mechanisms in morphogenesis, quantitative bioelectric models, identification of minimal experimental setups, and advancements in bioelectric modulation techniques relevant to regenerative medicine and cancer therapy. Ultimately, this research aims to utilize bioelectric signaling to develop new biomedical and bioengineering applications.

Traditional top-down robotic design often lacks the adaptability needed to handle real-world complexities, prompting the need for more flexible approaches. Therefore, this study introduces a novel cellular plasticity model tailored for bottom-up robotic design. The proposed model utilizes an activator-inhibitor reaction, a common foundation of Turing patterns, which are fundamental in morphogenesis -- the emergence of form from simple interactions. Turing patterns describe how diffusion and interactions between two chemical substances-an activator and an inhibitor-can lead to complex patterns and structures, such as the formation of limbs and feathers. Our study extends this concept by modeling cellular plasticity as an activator-inhibitor reaction augmented with environmental stimuli, encapsulating the core phenomena observed across various cell types: stem cells, neurons, and muscle cells. In addition to demonstrating self-regulation and self-containment, this approach ensures that a robot's form and function are direct emergent responses to its environment without a comprehensive environmental model. In the proposed model, a factory acts as the activator, producing a product that serves as the inhibitor, which is then influenced by environmental stimuli through consumption. These components are regulated by cellular plasticity phenomena as feedback loops. We calculate the equilibrium points of the model and the stability criterion. Simulations examine how varying parameters affect the system's transient behavior and the impact of competing functions on its functional capacity. Results show the model converges to a single stable equilibrium tuned to the environmental stimulation. Such dynamic behavior underscores the model's utility for generating predictable responses within robotics and biological systems, showcasing its potential for navigating the complexities of adaptive systems.

Information-theoretic fitness functions are becoming increasingly popular to produce generally useful, task-independent behaviors. One such universal function, dubbed empowerment, measures the amount of control an agent exerts on its environment via its sensorimotor system. Specifically, empowerment attempts to maximize the mutual information between an agent's actions and its received sensor states at a later point in time. Traditionally, empowerment has been applied to a conventional sensorimotor apparatus, such as a robot. Here, we expand the approach to a distributed, multi-agent sensorimotor system embodied by a neural cellular automaton (NCA). We show that the addition of empowerment as a secondary objective in the evolution of NCA to perform the task of morphogenesis, growing and maintaining a pre-specified shape, results in higher fitness compared to evolving for morphogenesis alone. Results suggest there may be a synergistic relationship between morphogenesis and empowerment. That is, indirectly selecting for coordination between neighboring cells over the duration of development is beneficial to the developmental process itself. Such a finding may have applications in developmental biology by providing potential mechanisms of communication between cells during growth from a single cell to a multicellular, target morphology. Source code for the experiments in this paper can be found at: \url{https://github.com/caitlingrasso/empowered-nca}.

Understanding the rules underlying organismal development is a major unsolved problem in biology. Each cell in a developing organism responds to signals in its local environment by dividing, excreting, consuming, or reorganizing, yet how these individual actions coordinate over a macroscopic number of cells to grow complex structures with exquisite functionality is unknown. Here we use recent advances in automatic differentiation to discover local interaction rules and genetic networks that yield emergent, systems-level characteristics in a model of development. We consider a growing tissue with cellular interactions are mediated by morphogen diffusion, differential cell adhesion and mechanical stress. Each cell has an internal genetic network that it uses to make decisions based on its local environment. We show that one can simultaneously learn parameters governing the cell interactions and the genetic network for complex developmental scenarios, including the symmetry breaking of an embryo from an initial cell, the creation of emergent chemical gradients,homogenization of growth via mechanical stress, programmed growth into a prespecified shape, and the ability to repair from damage. When combined with recent experimental advances measuring spatio-temporal dynamics and gene expression of cells in a growing tissue, the methodology outlined here offers a promising path to unravelling the cellular basis of development.

Morphological development into evolutionary patterns under structural instability is ubiquitous in living systems and often of vital importance for engineering structures. Here we propose a data-driven approach to understand and predict their spatiotemporal complexities. A machine-learning framework is proposed based on the physical modeling of morphogenesis triggered by internal or external forcing. Digital libraries of structural patterns are constructed from the simulation data, which are then used to recognize the abnormalities, predict their development, and assist in risk assessment and prognosis. The capabilities to identify the key bifurcation characteristics and predict the history-dependent development from the global and local features are demonstrated by examples of brain growth and aerospace structural design, which offer guidelines for disease diagnosis/prognosis and instability-tolerant design.