Related papers: The GraftalLace Cellular Automaton
We present ongoing work on a tool that consists of two parts: (i) A raw micro-level abstract world simulator with an interface to (ii) a 3D game engine, translator of raw abstract simulator data to photorealistic graphics. Part (i)…
If M is a monoid (e.g. the lattice Z^D), and G is a finite (nonabelian) group, then G^M is a compact group; a `multiplicative cellular automaton' (MCA) is a continuous transformation F:G^M-->G^M which commutes with all shift maps, and where…
Reversible Cellular Automata (RCA) are a physics-like model of computation consisting of an array of identical cells, evolving in discrete time steps by iterating a global evolution G. Further, G is required to be shift-invariant (it acts…
In this paper, we propose a new approach for building cellular automata to solve real-world segmentation problems. We design and train a cellular automaton that can successfully segment high-resolution images. We consider a colony that…
We describe a cellular-automaton based, two-dimensional (2D) lattice model which generates global oscillations in the EEG spectrum as well as time series of local field potentials resembling those observed during slow wave sleep. This is…
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…
We extend the usual definition of cellular automaton on a group in order to deal with a new kind of cellular automata, like cellular automata in the hyperbolic plane and we explore some properties of these cellular automata. This definition…
We make a detailed study of the infinite dimensional Galilean Conformal Algebra (GCA) in the case of two spacetime dimensions. Classically, this algebra is precisely obtained from a contraction of the generators of the relativistic…
Cellular automata (CAs) are notable computational models exhibiting rich dynamics emerging from the local interaction of cells arranged in a regular lattice. Graph CAs (GCAs) generalise standard CAs by allowing for arbitrary graphs rather…
A one-dimensional two-state number-conserving cellular automaton (NCCA) is a cellular automaton whose states are 0 or 1 and where cells take states 0 and 1 and updated their states by the rule which keeps overall sum of states constant. It…
A quantum cellular automaton (QCA) is an abstract model consisting of an array of finite-dimensional quantum systems that evolves in discrete time by local unitary operations. Here we propose a simple coarse-graining map, where the spatial…
We show that certain representations of graphs by operators on Hilbert space have uses in signal processing and in symbolic dynamics. Our main result is that graphs built on automata have fractal characteristics. We make this precise with…
In this paper, we mainly study linear one-dimensional and two-dimensional elementary cellular automata that generate symmetrical spatio-temporal patterns. For spatio-temporal patterns of cellular automata from the single site seed, we…
This contribution belongs to a combinatorial approach to hyperbolic geometry and it is aimed at possible applications to computer simulations. It is based on the splitting method which was introduced by the author and which is reminded in…
Cellular automata (CA) captivate researchers due to teh emergent, complex individualized behavior that simple global rules of interaction enact. Recent advances in the field have combined CA with convolutional neural networks to achieve…
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 construct a one-dimensional uniquely ergodic cellular automaton which is not nilpotent. This automaton can perform asymptotically infinitely sparse computation, which nevertheless never disappears completely. The construction builds on…
Lattice geometry profoundly shapes physical phenomena such as subsystem symmetry and directed percolation (DP). Among various lattice geometries, hyperbolic lattices are characterized by constant negative curvature and non-Abelian…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…
This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…