Related papers: On the classifiability of cellular automata
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…
A novel, information-based classification of elementary cellular automata is proposed that circumvents the problems associated with isolating whether complexity is in fact intrinsic to a dynamical rule, or if it arises merely as a product…
We describe a class of cellular automata (CAs) that are end-to-end differentiable. DCAs interpolate the behavior of ordinary CAs through rules that act on distributions of states. The gradient of a DCA with respect to its parameters can be…
This paper is the second part of a series of two papers dealing with bulking: a way to define quasi-order on cellular automata by comparing space-time diagrams up to rescaling. In the present paper, we introduce three notions of simulation…
A new class of automata networks is defined. Their evolution rules are determined by a probability measure p on the set of all integers Z and an indicator function I_A on the interval [0,1]. It is shown that any cellular automaton rule can…
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…
We study the predictability of emergent phenomena in complex systems. Using nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's…
We classify quantum cellular automata whose cells are qubits, on hypercubic lattices $\mathbb Z^s$, with the von Neumann neighborhood scheme, in terms of realizability as finite-depth quantum circuits. We show the most general structure of…
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…
We present a new classification of elementary cellular automata. It is based on the structure of the network of states, connected with the transitions between them; the latter are determined by the automaton rule. Recently an algorithm has…
In this paper we present a systematic view of Quantum Cellular Automata (QCA), a mathematical formalism of quantum computation. First we give a general mathematical framework with which to study QCA models. Then we present four different…
Conway's Game of Life is the best-known cellular automaton. It is a classic model of emergence and self-organization, it is Turing-complete, and it can simulate a universal constructor. The Game of Life belongs to the set of semi-totalistic…
In order to develop systems capable of artificial evolution, we need to identify which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical…
The emerging field of Nominal Computation Theory is concerned with the theory of Nominal Sets and its applications to Computer Science. We investigate here the impact of nominal sets on the definition of Cellular Automata and on their…
The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite…
Motivated by questions in biology and distributed computing, we investigate the behaviour of particular cellular automata, modelled as one-dimensional arrays of identical finite automata. We investigate what sort of self-stabilising…
Cellular automata are capable of developing complex behaviors based on simple local interactions between their elements. Some of these characteristics have been used to propose and improve meta-heuristics for global optimization; however,…
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…
Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for…
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…