Related papers: Further travels with my ant
This is a study of the one-dimensional elementary cellular automaton rule 54 in the new formalism of "flexible time". We derive algebraic expressions for groups of several cells and their evolution in time. With them we can describe the…
Modeling the immune system so that its essential functionalities stand out without the need for every molecular or cellular interaction to be taken into account has been challenging for many decades. Two competing approaches have been the…
Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial…
An elementary cellular automaton with memory is a chain of finite state machines (cells) updating their state simultaneously and by the same rule. Each cell updates its current state depending on current states of its immediate neighbours…
We consider a probabilistic cellular automaton to analyze the stochastic dynamics of a predator-prey system. The local rules are Markovian and are based in the Lotka-Volterra model. The individuals of each species reside on the sites of a…
We prove the equivalence of two classes of counter machines and one class of distributed automata. Our counter machines operate on finite words, which they read from left to right while incrementing or decrementing a fixed number of…
The motility of a fish keratocyte on a flat substrate exhibits two distinct regimes: the non-migrating and the migrating one. In both configurations the shape is fixed in time and, when the cell is moving, the velocity is constant in…
An automata network (AN) is a finite graph where each node holds a state from a finite alphabet and is equipped with a local map defining the evolution of the state of the node depending on its neighbors. The global dynamics of the network…
One usually thinks of a cat moving from one room to another in an apartment as random walk model. Imagine now that it also has the possibility to go from one apartment to another by crossing some corridors. That yields a new probabilistic…
Discretizing spacetime is often a natural step towards modelling physical systems. For quantum systems, if we also demand a strict bound on the speed of information propagation, we get quantum cellular automata (QCAs). These originally…
In this paper, we prove that there is a strongly universal cellular automaton on the pentagrid with six states. For each cell c, Moore neighbourhood consists of the cells which share a vertex with c. Moreover, the rules are rotation…
The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most of the cases. In this article, we introduce…
The goal of this paper is to show why the framework of communication complexity seems suitable for the study of cellular automata. Researchers have tackled different algorithmic problems ranging from the complexity of predicting to the…
Using a simple model for the trail formation of ants, the relation between i)the schedule of feeding which represents the unsteady natural environment, ii)emerging patterns of trails connecting a nest with food resources, and iii)the…
Collective behavior of active elements inspired by mass of biological organisms is addressed. Especially, two topics are focused on among amazing behaviors performed by colony of ants. First, task allocation phenomena are treated from the…
We theoretically predict and experimentally demonstrate that several different particle species can be separated from each other by means of a ratchet device, consisting of periodically arranged triangular (ratchet) shaped obstacles. We…
Can we quantify the change of complexity throughout evolutionary processes? We attempt to address this question through an empirical approach. In very general terms, we simulate two simple organisms on a computer that compete over limited…
The ants process is a stochastic process introduced by Kious, Mailler and Schapira as a model for the phenomenon of ants finding shortest paths between their nest and a source of food (seen as two marked nodes in a finite graph), with no…
Periodicity and relaxation are investigated for the trajectories of the states in one-dimensional finite cellular automata with rule-90 and 150. The time evolutions are described with matrices. Eigenvalue analysis is applied to clarify the…
A simple model is studied for the chemotactic movement of biological cells in the presence of a periodic chemical wave. It incorporates the feature of adaptation that may play an important role in allowing for ``rectified" chemotaxis:…