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Cellular automata (CA) have been found as an attractive modeling tool for various applications, such as, pattern recognition, image processing, data compression, encryption, and specially for VLSI design & test. For such applications,…
A family of multi-value cellular automaton (CA) associated with traffic flow is presented in this paper. The family is obtained by extending the rule-184 CA, which is an ultradiscrete analogue to the Burgers equation. CA models in the…
We consider Clifford Quantum Cellular Automata (CQCAs) and their time evolution. CQCAs are an especially simple type of Quantum Cellular Automata, yet they show complex asymptotics and can even be a basic ingredient for universal quantum…
This report investigates the history and impact of Generative Models and Connected and Automated Vehicles (CAVs), two groundbreaking forces pushing progress in technology and transportation. By focusing on the application of generative…
For any group $G$ and any set $A$, a cellular automaton (CA) is a transformation of the configuration space $A^G$ defined via a finite memory set and a local function. Let $\text{CA}(G;A)$ be the monoid of all CA over $A^G$. In this paper,…
The cellular automata discrete dynamical system is considered as the two-stage process: the majority rule for the change in the automata state and the rule for the change in topological relations between automata. The influence of changing…
This paper studies directional dynamics in cellular automata, a formalism previously introduced by the third author. The central idea is to study the dynamical behaviour of a cellular automaton through the conjoint action of its global rule…
This paper proposes several algorithms and their Cellular Automata Machine (CAM) for drawing the State Transition Diagram (STD) of an arbitrary Cellular Automata (CA) Rule (any neighborhood, uniform/ hybrid and null/ periodic boundary) and…
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…
Quantum-dot Cellular Automata (QCA) provides a basis for classical computation without transistors. Many simulations of QCA rely upon the so-called Intercellular Hartree Approximation (ICHA), which neglects the possibility of entanglement…
Understanding cellular mechanisms requires integrating information across DNA, RNA, and protein - the three molecular systems linked by the Central Dogma of molecular biology. While domain-specific foundation models have achieved success…
The Cellular Automaton (CA) modeling and simulation of solid dynamics is a long-standing difficult problem. In this paper we present a new two-dimensional CA model for solid dynamics. In this model the solid body is represented by a set of…
Within the class of stochastic cellular automata models of traffic flows, we look at the velocity dependent randomization variant (VDR-TCA) whose parameters take on a specific set of extreme values. These initial conditions lead us to the…
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…
The quantum cellular automata (QCA) effect is a transition in which multiple electron move coordinately by Coulomb interactions and observed in multiple quantum dots. This effect will be useful for realizing and improving quantum cellular…
For a group $G$ and a finite set $A$, a cellular automaton is a transformation of the configuration space $A^G$ defined via a finite neighborhood and a local map. Although neighborhoods are not unique, every CA admits a unique minimal…
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…
For any group $G$ and set $A$, a cellular automaton over $G$ and $A$ is a transformation $\tau : A^G \to A^G$ defined via a finite neighborhood $S \subseteq G$ (called a memory set of $\tau$) and a local function $\mu : A^S \to A$. In this…
Reversible Cellular Automata (RCA) are a particular kind of shift-invariant transformations characterized by a dynamics composed only of disjoint cycles. They have many applications in the simulation of physical systems, cryptography and…
Cellular automata are dynamical systems defined on lattices and commuting with the Bernoulli shift. In this work, we focus on the spectral properties of D-dimensional cellular automata. We give a characterization of their spectrum from both…