Related papers: Mathematical Physics of Cellular Automata
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…
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 $\lambda$.…
We define and study a few properties of a class of random automata networks. While regular finite one-dimensional cellular automata are defined on periodic lattices, these automata networks, called randomized cellular automata, are defined…
Deep learning techniques have recently demonstrated broad success in predicting complex dynamical systems ranging from turbulence to human speech, motivating broader questions about how neural networks encode and represent dynamical rules.…
A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…
This paper examines the claim that cellular automata (CA) belonging to Class III (in Wolfram's classification) are capable of (Turing universal) computation. We explore some chaotic CA (believed to belong to Class III) reported over the…
We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do…
We extend Cellular Automata to time-varying discrete geometries. In other words we formalize, and prove theorems about, the intuitive idea of a discrete manifold which evolves in time, subject to two natural constraints: the evolution does…
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…
Cellular automata can show well known features of quantum mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schroedinger equation. This includes corresponding conservation laws.…
Classical Cellular Automata (CCAs) are a powerful computational framework widely used to model complex systems driven by local interactions. Their simplicity lies in the use of a finite set of states and a uniform local rule, yet this…
A new formulation of special relativity is described. It is based on a postulate that the universe is a vast Cellular Automata (CA). We show that any CA model automatically leads to a maximum speed limit for the transfer of information from…
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
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…
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…
Number-conserving cellular automata (NCCA) are particularly interesting, both because of their natural appearance as models of real systems, and because of the strong restrictions that number-conservation implies. Here we extend the…
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular…
Individual cellular automata rules are attractive models for a range of biological and physical self-assembling systems. While coexpression and coevolution are common in such systems, ensembles of cellular automata rules remain poorly…