Related papers: The Toothpick Sequence and Other Sequences from Ce…
Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for…
A random planar quadrangulation process is introduced as an approximation for certain cellular automata in terms of random growth of rays from a given set of points. This model turns out to be a particular (rectangular) case of the…
Our main goal is to study a class of processes whose increments are generated via a cellular automata rule. Given the increments of a simple biased random walk, a new sequence of (dependent) Bernoulli random variables is produced. It is…
The articulation process of dynamical networks is studied with a functional map, a minimal model for the dynamic change of relationships through iteration. The model is a dynamical system of a function $f$, not of variables, having a…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
We study the $k$-Bonacci word over the infinite alphabet $\mathbb{N}$. Since the alphabet is infinite, the usual factor complexity is infinite and does not provide any information. We therefore investigate factor occurrence statistics in…
In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy,…
Using a group-theoretic approach, a method for determining the equivalence classes (also called orbits) of the set of rules of one-dimensional cellular automata induced by the symmetry operations of reflection and permutation and their…
It is well-known that the spacetime diagrams of some cellular automata have a fractal structure: for instance Pascal's triangle modulo 2 generates a Sierpinski triangle. It has been shown that such patterns can occur when the alphabet is…
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…
This paper proposes a new pattern of two dimensional cellular automata linear rules that are used for efficient edge detection of an image. Since cellular automata is inherently parallel in nature, it has produced desired output within a…
An additive cellular automaton is a linear map on the set of infinite multidimensional arrays of elements in a finite cyclic group $\mathbb{Z}/m\mathbb{Z}$. In this paper, we consider simplices appearing in the orbits generated from…
A Skolem sequence is a linear arrangement of the multiset, {1, 1, 2, 2, ..., n, n} such that if r in [n] appears in positions i and j, then |i-j| = r. We first translate the problem to a particular set of perfect matchings, then apply the…
In this paper, we look at two ways to implement determinisitic one dimensional cellular automata into hyperbolic cellular automata in three contexts: the pentagrid, the heptagrid and the dodecagrid, these tilings being classically denoted…
In the fields of computation and neuroscience, much is still unknown about the underlying computations that enable key cognitive functions including learning, memory, abstraction and behavior. This paper proposes a mathematical and…
This contribution belongs to a combinatorial approach to hyperbolic geometry and it is aimed at possible applications to computer simulations. It is based on the splitting method which was introduced by the author and which is reminded in…
Let L be an infinite regular language on a totally ordered alphabet (A,<). Feeding a finite deterministic automaton (with output) with the words of L enumerated lexicographically with respect to < leads to an infinite sequence over the…
We revisit the long-neglected problem of sequential circuit constructions from regular expressions. The class of languages that are recognized by sequential circuits is equivalent to the class of regular languages. This fact is shown in [5]…
A cellular automaton (CA) is a parallel synchronous computing model, which consists in a juxtaposition of finite automata (cells) whose state evolves according to that of their neighbors. Its trace is the set of infinite words representing…
We consider the problem of exhaustively visiting all pairs of linear cellular automata which give rise to orthogonal Latin squares, i.e., linear Orthogonal Cellular Automata (OCA). The problem is equivalent to enumerating all pairs of…