Related papers: Simulation of Gacs' Automaton
In this article, we discuss the family of cellular automata generated by so-called idempotent cellular automata (CA G such that G^2 = G) on the full shift. We prove a characterization of products of idempotent CA, and show examples of CA…
This paper presents GARCON program, illustrating its functionality on a simple HEP analysis example. The program automatically performs rectangular cuts optimization and verification for stability in a multi-dimensional phase space. The…
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…
This paper presents a rotation-invariant embedded platform for simulating (neural) cellular automata (NCA) in modular robotic systems. Inspired by previous work on physical NCA, we introduce key innovations that overcome limitations in…
We introduce a quantum cellular automaton that achieves approximate phase-covariant cloning of qubits. The automaton is optimized for 1-to-2N economical cloning. The use of the automaton for cloning allows us to exploit different foliations…
A cellular automaton that is a generalization of the box-ball system with either many kinds of balls or finite carrier capacity is proposed and studied through two discrete integrable systems: nonautonomous discrete KP lattice and…
In the article a transition from pattern evolution equation of reaction-diffusion type to a cellular automaton (CA) is described. The applicability of CA is demonstrated by generating patterns of complex irregular structure on a hexagonal…
This research describes a three dimensional quantum cellular automaton (QCA) which can simulate all other 3D QCA. This intrinsically universal QCA belongs to the simplest subclass of QCA: Partitioned QCA (PQCA). PQCA are QCA of a particular…
We simulate self-reproducing micellar systems using a recently introduced lattice-gas automaton. This dynamical model correctly describes the equilibrium and non-equilibrium properties of mixtures of oil, water and surfactants. The…
Video games can be used as an excellent test bed for Artificial Intelligence (AI) techniques. They are challenging and non-deterministic, this makes it very difficult to write strong AI players. An example of such a video game is Ms.…
Cellular Automata (CA) are a class of discrete dynamical systems that have been widely used to model complex systems in which the dynamics is specified at local cell-scale. Classically, CA are run on a regular lattice and with perfect…
This note is a survey of examples and results about cellular automata with the purpose of recalling that there is no 'universal' way of being computationally universal. In particular, we show how some cellular automata can embed efficient…
This study presents a unitary quantum cellular automaton (QCA) that, in the continuum limit, converges to the (1+1)-dimensional Generalized Dirac Equation (GDE). We outline the construction of the unitary, discrete-time evolution and derive…
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…
Neural Cellular Automata (NCAs) have been proven effective in simulating morphogenetic processes, the continuous construction of complex structures from very few starting cells. Recent developments in NCAs lie in the 2D domain, namely…
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…
Inspired by biological and cultural evolution, there have been many attempts to explore and elucidate the necessary conditions for open-endedness in artificial intelligence and artificial life. Using a continuous cellular automata called…
Cellular automata are a class of computational models based on simple rules and algorithms that can simulate a wide range of complex phenomena. However, when using conventional computers, these 'simple' rules are only encapsulated at the…
The advantage of Cellular Potts Model (CPM) is due to its ability for introducing cell-cell interaction based on the well known statistical model i.e. the Potts model. On the other hand, Lattice gas Cellular Automata (LGCA) can simulate…
We reproduce apparently complex cellular automaton behaviour with simple partial differential equations as developed in (Keane 09). Our PDE model easily explains behaviour observed in selected scenarios of the cellular automaton wargame…