Related papers: Balanced simplices
Factorized dynamics in soliton cellular automata with quantum group symmetry is identified with a motion of particles and anti-particles exhibiting pair creation and annihilation. An embedding scheme is presented showing that the…
We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of left homogeneous spaces are spheres, Euclidean spaces, as…
This note is a survey of examples and results about cellular automata with the purpose of recalling that there is no 'universal' way of being computationally universal. In particular, we show how some cellular automata can embed efficient…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…
We show that a large number of elementary cellular automata are computationally simple. This work is the first systematic classification of elementary cellular automata based on a formal notion of computational complexity. Thanks to the…
We discuss the role of classical control in the context of reversible quantum cellular automata. Employing the structure theorem for quantum cellular automata, we give a general construction scheme to turn an arbitrary cellular automaton…
We introduce and study cellular automata whose cell spaces are left-homogeneous spaces. Examples of left-homogeneous spaces are spheres, Euclidean spaces, as well as hyperbolic spaces acted on by isometries; uniform tilings acted on by…
The transport and chemical reactions of solutes are modelled as a cellular automaton in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule. The model describes…
In this paper, we partially solve an open problem, due to J.C. Molluzzo in 1976, on the existence of balanced Steinhaus triangles modulo a positive integer $n$, that are Steinhaus triangles containing all the elements of…
Periodic lattices have been widely explored for decades, owing to their peculiar vibrational behavior. On the other hand, certain types of aperiodic lattices have enabled new phenomena that may not be otherwise attainable in periodic ones.…
In this paper, the author aims to establish a mathematical model for a mimic computer. To this end, a novel automaton is proposed. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a…
Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional…
We add small random perturbations to a cellular automaton and consider the one-parameter family $(F_\epsilon)_{\epsilon>0}$ parameterized by $\epsilon$ where $\epsilon>0$ is the level of noise. The objective of the article is to study the…
Since first introduced by John von Neumann, the notion of cellular automaton has grown into a key concept in computer science, physics and theoretical biology. In its classical setting, a cellular automaton is a transformation of the set of…
We are entering a new era in which software systems are becoming more and more complex and larger. So, the composition of such systems is becoming infeasible by manual means. To address this challenge, self-organising software models…
This is a study of localised structures in one-dimensional cellular automata, with the elementary cellular automaton Rule 54 as a guiding example. A formalism for particles on a periodic background is derived, applicable to all…
In this paper we study the structure of cellular pseudomanifolds (aka abstract polytopes). These are natural combinatorial generalisations of polytopal spheres (i.e., boundary complexes of convex polytopes). This class is closed under…
We study real numbers defined by multidimensional automatic arrays weighted by multiplicatively independent bases. Let $a_1, \dots, a_r\geq 2$ be integers such that $\log a_1, \dots, \log a_r$ are $\mathbb Q$-linearly independent. Given…
The trace subshift of a cellular automaton is the subshift of all possible columns that may appear in a space-time diagram, ie the infinite sequence of states of a particular cell of a configuration; in the language of symbolic dynamics one…