元胞自动机与格子气

Two kinetic exchange models are proposed to explore the dynamics of closed economic markets characterized by random exchanges, saving propensities, and collective transactions. Model I simulates a system where individual transactions occur…

Elementary cellular automata (ECA) are converted into multiplicative versions by using permuted n-dim Galois fields and octonion multiplication tables as binary pointers to each rule's Wolfram code truth table. This enables an extension of…

Self-organizing complex systems can be modeled using cellular automaton models. However, the parametrization of these models is crucial and significantly determines the resulting structural pattern. In this research, we introduce and…

Cellular automata are computers, similar to Turing machines. The main difference is that Turing machines use a one-dimensional tape, whereas cellular automata use a two-dimensional grid. The best-known cellular automaton is the Game of…

We propose a simple mathematical model to describe the mechanical relaxation of cells within a curved epithelial tissue layer represented by an arbitrary curve in two-dimensional space. This model generalises previous one-dimensional models…

The year of 2024 marks the 25th anniversary of the publication of evoloops, an evolutionary variant of Chris Langton's self-reproducing loops which proved constructively that Darwinian evolution of self-reproducing organisms by variation…

Andrei Toom, who died in September 2022, contributed some of the most fundamental results on probabilistic cellular automata. We want to acquaint the reader with these and will also try to give the reader a look at the environment in which…

Finite cellular automata (FCA) are widely used in simulating nonlinear complex systems, and their reversibility is closely related to information loss during the evolution. However, only a relatively small portion of their reversibility…

Conways Game of Life is a cellular automaton noted for its rich, complex, and emergent behavior, which seems qualitatively lifelike it exists within a wider space of different rule-sets of cellular automata none of which have been found to…

Cellular automata represent physical systems where both space and time are discrete, and the associated physical quantities assume a limited set of values. While previous research has applied cellular automata in modeling chemical,…

We propose a simple cellular automaton model of a self-healing system and investigate its properties. In the model, the substrate is a two-dimensional checkerboard configuration which can be damaged by changing values of a finite number of…

The objective is the design of a Cellular Automata rule that can form patterns with 'touching' loops. A loop is defined as a closed path of 1-cells in a 2D grid on a zero background and with a zero border. A path cell is connected with two…

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…

Cellular automata (CAs) and convolutional neural networks (CNNs) are closely related due to the local nature of information processing. The connection between these topics is beneficial to both related fields, for conceptual as well as…

Probabilistic Cellular Automata are a generalization of Cellular Automata. Despite their simple definition, they exhibit fascinating and complex behaviours. The stationary behaviour of these models changes when model parameters are varied,…

Elementary cellular automata are the simplest form of cellular automata, studied extensively by Wolfram in the 1980s. He discovered complex behavior in some of these automata and developed a classification for all cellular automata based on…

Like Life, Lenia CA support a range of patterns that move, interact with their environment, and/or are modified by said interactions. These patterns maintain a cohesive, self-organizing morphology, i.e. they exemplify autopoiesis, the…

Elementary Cellular Automata (ECA) are a well-studied computational universe that is, despite its simple configurations, capable of impressive computational variety. Harvesting this computation in a useful way has historically shown itself…

The Tile Automata (TA) model describes self-assembly systems in which monomers can build structures and transition with an adjacent monomer to change their states. This paper shows that seeded TA is a non-committal intrinsically universal…

Understanding employee behavior in a workplace is critical for enhancing overall organizational performance. Despite numerous efforts to improve work environments, many organizations still need help with challenges primarily rooted in…