Related papers: Efficient Simulation of Non-uniform Cellular Autom…
This work studies some aspects of the computational power of fully asynchronous cellular automata (ACA). We deal with some notions of simulation between ACA and Turing Machines. In particular, we characterize the updating sequences…
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…
Neural Cellular Automata (NCAs) are bio-inspired dynamical systems in which identical cells iteratively apply a learned local update rule to self-organize into complex patterns, exhibiting regeneration, robustness, and spontaneous dynamics.…
Deep learning techniques have recently demonstrated broad success in predicting complex dynamical systems ranging from turbulence to human speech, motivating broader questions about how neural networks encode and represent dynamical rules.…
Cellular Automata (CA) have long been foundational in simulating dynamical systems computationally. With recent innovations, this model class has been brought into the realm of deep learning by parameterizing the CA's update rule using an…
Very recently, the Neural Cellular Automata (NCA) has been proposed to simulate the morphogenesis process with deep networks. NCA learns to grow an image starting from a fixed single pixel. In this work, we show that the neural network (NN)…
Cellular automaton (CA) approach is an important theoretical framework for studying complex system behavior and has been widely applied in various research field. CA traffic flow models have the advantage of flexible evolution rules and…
The original local, discrete example of Linear Unitary Cellular Automata (LUCA) is analyzed in terms of a new representation previously introduced in [1] for classical CA. Several important underlying symmetries are reviewed and their tight…
The emergent dynamics in spacetime diagrams of cellular automata (CAs) is often organised by means of a number of behavioural classes. Whilst classification of elementary CAs is feasible and well-studied, non-elementary CAs are generally…
The Reservoir Computing (RC) paradigm utilizes a dynamical system, i.e., a reservoir, and a linear classifier, i.e., a read-out layer, to process data from sequential classification tasks. In this paper the usage of Cellular Automata (CA)…
Neural Cellular Automata (NCA) models are trainable variations of traditional Cellular Automata (CA). Emergent motion in the patterns created by NCA has been successfully applied to synthesize dynamic textures. However, the conditions…
The dynamical behavior of non-uniform cellular automata is compared with the one of classical cellular automata. Several differences and similarities are pointed out by a series of examples. Decidability of basic properties like…
Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of…
Cellular automata (CA) models are widely used to simulate complex systems with emergent behaviors, but identifying hidden parameters that govern their dynamics remains a significant challenge. This study explores the use of Convolutional…
We study the class of asynchronous non-uniform cellular automata (ANUCA) over an arbitrary group universe with multiple local transition rules. We introduce the notion of stable injectivity, stable reversibility, stable post-surjectivity…
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…
Cellular automata (CA) captivate researchers due to teh emergent, complex individualized behavior that simple global rules of interaction enact. Recent advances in the field have combined CA with convolutional neural networks to achieve…
Biological neural networks are often modeled as systems of coupled, nonlinear, ordinary or partial differential equations. The number of differential equations used to model a network increases with the size of the network and the level of…
Neural Cellular Automata (NCAs) have been proven effective in simulating morphogenetic processes, the continuous construction of complex structures from very few starting cells. Recent developments in NCAs lie in the 2D domain, namely…
Neural cellular automata (Neural CA) are a recent framework used to model biological phenomena emerging from multicellular organisms. In these systems, artificial neural networks are used as update rules for cellular automata. Neural CA are…