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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…

Neural and Evolutionary Computing · Computer Science 2024-06-17 Aidan Barbieux , Rodrigo Canaan

The development of LLMs has elevated AI agents from task-specific tools to long-lived, decision-making entities. Yet, most architectures remain static and reactive, tethered to manually defined, narrow scenarios. These systems excel at…

Artificial Intelligence · Computer Science 2025-12-23 Mingyang Sun , Feng Hong , Weinan Zhang

Agents based on Large Language Models (LLMs) are increasingly permeating various domains of human production and life, highlighting the importance of aligning them with human values. The current alignment of AI systems primarily focuses on…

Computation and Language · Computer Science 2024-02-21 Shimin Li , Tianxiang Sun , Qinyuan Cheng , Xipeng Qiu

The research field of Artificial Life studies how life-like phenomena such as autopoiesis, agency, or self-regulation can self-organize in computer simulations. In cellular automata (CA), a key open-question has been whether it it is…

Multiagent Systems · Computer Science 2024-02-19 Gautier Hamon , Mayalen Etcheverry , Bert Wang-Chak Chan , Clément Moulin-Frier , Pierre-Yves Oudeyer

The generation of sustained, open-ended complexity from local interactions remains a fundamental challenge in artificial life. Differentiable multi-agent systems, such as Petri Dish Neural Cellular Automata (PD-NCA), exhibit rich…

Neural and Evolutionary Computing · Computer Science 2026-04-14 Uljad Berdica , Jakob Foerster , Frank Hutter , Arber Zela

Results of experimental investigation are presented of evolutionary dynamics of several stochastic pattern formation and growth models designed by modifications of the famous mathematical Game of Life. The modifications are two-fold: Game…

Cellular Automata and Lattice Gases · Physics 2013-10-30 Leonid Yaroslavsky

Let A:={0,1}. A `cellular automaton' (CA) is a shift-commuting transformation of A^{Z^D} determined by a local rule. Likewise, a `Euclidean automaton' is a shift-commuting transformation of A^{R^D} determined by a local rule. `Larger than…

Dynamical Systems · Mathematics 2007-05-23 Marcus Pivato

Evolution, the engine behind the survival and growth of life on Earth, operates through the population-based process of reproduction. Inspired by this principle, this paper formally defines a newly emerging problem -- the population-based…

Computation and Language · Computer Science 2025-03-10 Yiqun Zhang , Peng Ye , Xiaocui Yang , Shi Feng , Shufei Zhang , Lei Bai , Wanli Ouyang , Shuyue Hu

Without loss of generalisation to other systems, including possibly non-deterministic ones, we demonstrate the application of methods drawn from algorithmic information dynamics to the characterisation and classification of emergent and…

Cellular Automata and Lattice Gases · Physics 2018-04-09 Hector Zenil , Narsis A. Kiani , Jesper Tegnér

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 and Lattice Gases · Physics 2020-01-20 William Gilpin

Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically)…

Discrete Mathematics · Computer Science 2009-02-10 Laurent Boyer , Guillaume Theyssier

A Cellular Automata (CA) rule is presented that can generate "loop patterns" in a 2D grid under fixed boundary conditions. A loop is a cyclically closed path represented by one-cells enclosed by zero-cells. A loop pattern can contain…

Cellular Automata and Lattice Gases · Physics 2025-05-30 Rolf Hoffmann , Mariusz Białecki

Large Language Models (LLMs) have unveiled remarkable capabilities in understanding and generating both natural language and code, but LLM reasoning is prone to hallucination and struggle with complex, novel scenarios, often getting stuck…

Neural and Evolutionary Computing · Computer Science 2025-05-12 Antonio Jimeno Yepes , Pieter Barnard

A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new…

Cellular Automata and Lattice Gases · Physics 2010-03-26 Xin-She Yang , Young Z. L. Yang

The searching for the stable patterns in the evolution of cellular automata is implemented using stochastic synchronization between the present structures of the system and its precedent configurations. For most of the known evolution rules…

Cellular Automata and Lattice Gases · Physics 2007-05-23 J. R. Sanchez , R. Lopez-Ruiz

This paper introduces Differentiable Logic Cellular Automata (DiffLogic CA), a novel combination of Neural Cellular Automata (NCA) and Differentiable Logic Gates Networks (DLGNs). The fundamental computation units of the model are…

Artificial Intelligence · Computer Science 2025-06-06 Pietro Miotti , Eyvind Niklasson , Ettore Randazzo , Alexander Mordvintsev

A profound challenge for A-Life is to construct agents whose behavior is 'life-like' in a deep way. We propose an architecture and approach to constructing networks driving artificial agents, using processes analogous to the processes that…

Neural and Evolutionary Computing · Computer Science 2022-02-01 Addison Wood , Jory Schossau , Nick Sabaj , Richard Liu , Mark Reimers

A number-conserving cellular automaton is a simplified model for a system of interacting particles. This paper contains two related constructions by which one can find all one-dimensional number-conserving cellular automata with one kind of…

Cellular Automata and Lattice Gases · Physics 2023-06-22 Markus Redeker

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…

Cellular Automata and Lattice Gases · Physics 2018-10-09 Junfang Tian , Chenqiang Zhu , Rui Jiang

Discovering diverse visual patterns in continuous cellular automata (CA) is challenging due to the vastness and redundancy of high-dimensional behavioral spaces. Traditional exploration methods like Novelty Search (NS) expand locally by…

Artificial Intelligence · Computer Science 2025-09-05 Sina Khajehabdollahi , Gautier Hamon , Marko Cvjetko , Pierre-Yves Oudeyer , Clément Moulin-Frier , Cédric Colas