Related papers: Three-level description of the domino cellular aut…
Growth patterns generated by filamentous organisms (e.g. actinomycetes and fungi) involve spatial and temporal dynamics at different length scales. Several mathematical models have been proposed in the last thirty years to address these…
Complexity has been a recurrent research topic in cellular automata because they represent systems where complex behaviors emerge from simple local interactions. A significant amount of previous research has been conducted proposing…
How do cellular automata behave in the limit of a very large number of cells? Is there a continuum limit with simple properties? We attack this problem by mapping certain classes of automata to quantum field theories for which powerful…
We use Monte Carlo simulation to study the phase diagram of three-dimensional dynamical triangulations with a boundary. Three phases are indentified and characterized. One of these phases is a new, boundary dominated phase; a simple…
Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates…
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,…
Dynamic properties of a one-dimensional probabilistic cellular automaton are studied by monte-carlo simulation near a critical point which marks a second-order phase transition from a active state to a effectively unique absorbing state.…
We present applications of a cellular automaton approach to pedestrian dynamics introduced in [1,2]. It is shown that the model is able to reproduce collective effects and self-organization phenomena encountered in pedestrian traffic, e.g.…
The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the…
This article introduces new tools to study self-organisation in a family of simple cellular automata which contain some particle-like objects with good collision properties (coalescence) in their time evolution. We draw an initial…
We study a neural network model of interacting stochastic discrete two--state cellular automata on a regular lattice. The system is externally tuned to a critical point which varies with the degree of stochasticity (or the effective…
The asymptotic behavior of a cellular automaton iterated on a random configuration is well described by its limit probability measure(s). In this paper, we characterize measures and sets of measures that can be reached as limit points after…
We created two dimensional hexagonal cellular automata to obtain complexity. Considering the game of life rules, Wolfram's works about life-like structures and John von Neumann's self-replication, self-maintenance, self-reproduction…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
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…
A simple mechanism for the emergence of complexity in cellular automata out of predictable dynamics is described. This leads to unfold the concept of conditional predictability for systems whose trajectory can only be piecewise known. The…
The stochastic discrete space-time model of an immune response on tumor spreading in a two-dimensional square lattice has been developed. The immunity-tumor interactions are described at the cellular level and then transferred into the…
Classical cellular automata represent a class of explicit discrete spacetime lattice models in which complex large-scale phenomena emerge from simple deterministic rules. With the goal to uncover different physically distinct classes of…
In this paper we study the space evolution in the Rule 54 reversible cellular automaton, which is a paradigmatic example of a deterministic interacting lattice gas. We show that the spatial translation of time configurations of the…
There exists an index theory to classify strictly local quantum cellular automata in one dimension. We consider two classification questions. First, we study to what extent this index theory can be applied in higher dimensions via…