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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…
In this paper we present a quantization of Cellular Automata. Our formalism is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this…
Cellular automata, CA for short are continuous maps defined on the set of configurations over a finite alphabet A that commutes with the shift. They are characterized by the existence of local function which determine by local behavior the…
Cellular automata provide a fascinating class of dynamical systems capable of diverse complex behavior. These include simplified models for many phenomena seen in nature. Among other things, they provide insight into self-organized…
Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators to Turing-complete computation. We discover that quantum cellular automata (QCA) can exhibit complexity in…
We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a…
The subject of this paper is the evolution of the concept of information processing in regular structures based on multi-level processing in nested cellular automata. The essence of the proposed model is a discrete space-time containing…
One-dimensional cellular automata are discrete dynamical systems that operate on an infinite lattice of sites and are characterized by the locality and uniformity of their update rule. Permutations of the state set and isometric…
We introduce Network Automata, a framework which couples the topological evolution of a network to its structure. It is useful for dealing with networks in which the topology evolves according to some specified microscopic rules and,…
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…
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. Explaining the fractal structure of the spacetime diagrams of cellular…
Measuring similarity in urban spatial networks is key to understanding cities as complex systems. Yet most existing methods are not tailored for spatial networks and struggle to differentiate them effectively. We propose GCA-Sim, a…
In this paper, we look at the possibility to implement the algorithm to construct a discrete line devised by the first author in cellular automata. It turns out that such an implementation is feasible.
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…
Finite automata were used to determine multiple addresses in number systems and to find topological properties of self-affine tiles and finite type fractals. We join these two lines of research by axiomatically defining automata which…
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…
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…
The basis for most of the ideas mentioned in this paper is the theory of cellular automata. A cellular automata contains a regular grid of cells, with each cell having a pre-defined set of finite states. The initial state is determined at…
Cellular automata are discrete and computational models thatcan be shown as general models of complexity. They are used in varied applications to derive the generalized behavior of the presented model. In this paper we have took one such…
In addition to the $\lambda$ parameter, we have found another parameter which characterize the class III, class II and class IV patterns more quantitatively. It explains why the different classes of patterns coexist at the same $\lambda$.…