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A new paradigm for the unification of physics is described. It is called Cellular Automata (CA) theory, which is the most massively parallel computer model currently known to science. We maintain that at the tiniest distance and time scales…
In this exploratory paper we introduce the problem of cognitive agents that learn how to modify their environment according to local sensing to reach a global goal. We concentrate on discrete dynamics (cellular automata) on a…
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…
Cellular Automaton (CA) and an Integral Value Transformation (IVT) are two well established mathematical models which evolve in discrete time steps. Theoretically, studies on CA suggest that CA is capable of producing a great variety of…
In this paper, we explore relationships between two models of systems which are governed by only the local interactions of large collections of simple components: cellular automata (CA) and the abstract Tile Assembly Model (aTAM). While…
Models of areas of physics in terms of cellular automata have become increasingly popular. Cellular automata (CAs) support the modeling of systems with discrete state component values and enforce the comprehensive specification of the…
The essential ingredient for studying the phenomena of emergence is the ability to generate and manipulate emergent systems that span large scales. Cellular automata are the model class particularly known for their effective scalability but…
Two-dimensional nine neighbor hood rectangular Cellular Automata rules can be modeled using many different techniques like Rule matrices, State Transition Diagrams, Boolean functions, Algebraic Normal Form etc. In this paper, a new model is…
A digit function is presented which provides the $i$th-digit in base $p$ of any real number $x$. By means of this function, formulated within $\mathcal{B}$-calculus, the local, nonlocal and global dynamical behaviors of cellular automata…
Most current methods for identifying coherent structures in spatially-extended systems rely on prior information about the form which those structures take. Here we present two new approaches to automatically filter the changing…
Modeling the ability of multicellular organisms to build and maintain their bodies through local interactions between individual cells (morphogenesis) is a long-standing challenge of developmental biology. Recently, the Neural Cellular…
Classical Cellular Automata (CCAs) are a powerful computational framework widely used to model complex systems driven by local interactions. Their simplicity lies in the use of a finite set of states and a uniform local rule, yet this…
Exactly ergodicity in boundary-driven semi-infinite cellular automata (CA) are investigated. We establish all the ergodic rules in CA with 3, 4, and 5 states. We analytically prove the ergodicity for 12 rules in 3-state CA and 118320 rules…
Texture recognition is one of the most important tasks in computer vision and, despite the recent success of learning-based approaches, there is still need for model-based solutions. This is especially the case when the amount of data…
Cellular automata are widely used to model natural or artificial systems. Classically they are run with perfect synchrony, i.e., the local rule is applied to each cell at each time step. A possible modification of the updating scheme…
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,…
In this paper we study the dynamics of 1- and 2- dimensional cellular automata, using a 2-adic representation of the states, we give a simple graphical technique for finding periodic solutions. We also study the continuity properties of the…
This paper introduces a hierarchical cellular automaton (HCA)model for simulation of distributed self-organizing control of traffic signals at intersections in road network. The proposed HCA consists of three hierarchy levels that describe…
Cellular Automata (CAs) are computational models that can capture the essential features of systems in which global behavior emerges from the collective effect of simple components, which interact locally. During the last decades, CAs have…
This study introduces Skewed Fully Asynchronous Cellular Automata (SACA), a novel update scheme in cellular automata that updates the states of only two consecutive and adjacent cells, such as ci and ci+1, simultaneously at each time step.…