Related papers: Cellular automata, many-valued logic, and deep neu…
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on 2D CA and aims at showing that the situation is different and more…
In this dissertation, we study temporally stochasticity in cellular automata and the behavior of such cellular automata. The work also explores the computational ability of such cellular automaton that illustrates the computability of…
Large Language Models demonstrate remarkable mathematical capabilities but at the same time struggle with abstract reasoning and planning. In this study, we explore whether Transformers can learn to abstract and generalize the rules…
This study focuses on an extended model of a standard cellular automaton (CA) that includes an extra index consisting of a radius that defines a perception area for each cell in addition to the radius defined by the CA rule. Extended…
Complexity has been a recurrent research topic in cellular automata because they represent systems where complex behaviors emerge from simple local interactions. A significant amount of previous research has been conducted proposing…
Recent years have witnessed the great success of deep neural networks in many research areas. The fundamental idea behind the design of most neural networks is to learn similarity patterns from data for prediction and inference, which lacks…
Recurrent Neural Networks (RNNs) have been a prominent concept within artificial intelligence. They are inspired by Biological Neural Networks (BNNs) and provide an intuitive and abstract representation of how BNNs work. Derived from the…
The design of complex self-organising systems producing life-like phenomena, such as the open-ended evolution of virtual creatures, is one of the main goals of artificial life. Lenia, a family of cellular automata (CA) generalizing Conway's…
Cellular automata (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and…
Inspired by cellular growth and self-organization, Neural Cellular Automata (NCAs) have been capable of "growing" artificial cells into images, 3D structures, and even functional machines. NCAs are flexible and robust computational systems…
We propose that the behaviour of non-linear media can be controlled automatically through coevolutionary systems. By extension, forms of unconventional computing, i.e., massively parallel non-linear computers, can be realised by such an…
Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for…
We extend the theory of Cellular Automata to arbitrary, time-varying graphs. In other words we formalize, and prove theorems about, the intuitive idea of a labelled graph which evolves in time - but under the natural constraint that…
Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and…
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
Combining neural networks with continuous logic and multicriteria decision making tools can reduce the black box nature of neural models. In this study, we show that nilpotent logical systems offer an appropriate mathematical framework for…
Cellular automata generate spatially extended, temporally persistent emergent structures from local update rules. No general method derives the mechanisms of that generation from the rule itself; existing tools reconstruct structure from…
We study self-similarity in one-dimensional probabilistic cellular automata (PCA) using the renormalization technique. We introduce a general framework for algebraic construction of renormalization groups (RG) on cellular automata and apply…
Recent extensions of Cellular Automata (CA) have incorporated key ideas from modern deep learning, dramatically extending their capabilities and catalyzing a new family of Neural Cellular Automata (NCA) techniques. Inspired by…