Related papers: A class of cellular automata equivalent to determi…
In order to develop systems capable of modeling artificial life, 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…
For deterministic monotone cellular automata on the $d$-dimensional integer lattice, Toom has given necessary and sufficient conditions for the all-one fixed point to be stable against small random perturbations. The proof of sufficiency is…
The paper formalizes and extends the idea of local structure approximation for cellular automata originally proposed by Gutowitz et. al. We start with a review of the construction of a probability measure on the set of bi-infinite strings…
We investigate the density classification task (DCT) -- determining the majority bit in a one-dimensional binary lattice -- within a quantum cellular automaton (CA) framework. While there is no one-dimensional two-state, radius $r \geq 1$,…
The mechanism which discriminates the pattern classes at the same $\lambda$, is found. It is closely related to the structure of the rule table and expressed by the numbers of the rules which break the strings of the quiescent states. It is…
We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…
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 cellular automata model that describes as limit cases of his parameters the spread of contagious diseases modeled by systems of ordinary or partial differential equations is developed. Periodic features of the behavior of human settlement…
The cellular automata with local permutation invariance are considered. We show that in the two-state case the set of such automata coincides with the generalized Game of Life family. We count the number of equivalence classes of the rules…
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 generate spatially extended, temporally persistent emergent structures from local update rules. No general method derives the mechanisms of that generation from the rule itself; existing tools reconstruct structure from…
We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automata…
We study a two-dimensional cellular automaton (CA), called Diffusion Rule (DR), which exhibits diffusion-like dynamics of propagating patterns. In computational experiments we discover a wide range of mobile and stationary localizations…
Self-organizing complex systems can be modeled using cellular automaton models. However, the parametrization of these models is crucial and significantly determines the resulting structural pattern. In this research, we introduce and…
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…
While for synchronous deterministic cellular automata there is an accepted definition of reversibility, the situation is less clear for asynchronous cellular automata. We first discuss a few possibilities and then investigate what we call…
We study a two-dimensional semi-totalistic binary cell-state cellular automaton, which imitates a reversible precipitation in an abstract chemical medium. The systems exhibits a non-trivial growth and nucleation. We demonstrate how basic…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
The fixed point construction is a method for designing tile sets and cellular automata with highly nontrivial dynamical and computational properties. It produces an infinite hierarchy of systems where each layer simulates the next one. The…
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…