Related papers: Free fall and cellular automata
In this paper, we formalize precisely the sense in which the application of cellular automaton to partial configuration is a natural extension of its local transition function through the categorical notion of Kan extension. In fact, the…
We extend the theory of Cellular Automata to arbitrary, time-varying graphs. In other words we formalize, and prove theorems about, the intuitive idea of a labelled graph which evolves in time - but under the natural constraint that…
State-of-the-art review of cellular automata, cellular automata for partial differential equations, differential equations for cellular automata and pattern formation in biology and engineering.
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…
This text aims to provide a self-contained, comprehensive, and reasonably detailed presentation of the theory of Stallings automata and some of its main applications.
We propose and discuss two variants of kinetic particle models - cellular automata in 1+1 dimensions, which have some appeal due to their simplicity and intriguing properties which could warrant further research and applications. The first…
We analytically diagonalize a discrete-time on-site interacting fermionic cellular automaton in the two-particle sector. Important features of the solutions sensibly differ from those of analogous Hamiltonian models. In particular, we found…
Random boolean cellular automata are investigated, where each gate has two randomly chosen inputs and is randomly assigned a boolean function of its inputs. The effect of non-uniform distributions on the choice of the boolean functions is…
In recent years the modelling of traffic flow using methods from statistical physics, especially cellular automata models have allowed simulations of large traffic networks faster than real time. In this paper, we study a probabilistic…
Based on computer simulations Wolfram presented in several papers conjectured classifications of cellular automata into 4 types. He distinguishes the 4 classes of cellular automata by the evolution of the pattern generated by applying a…
Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial…
There exists an index theory to classify strictly local quantum cellular automata in one dimension. We consider two classification questions. First, we study to what extent this index theory can be applied in higher dimensions via…
We study the quantization of a model proposed by Newton to explain centripetal force namely, that of a particle moving on a regular polygon. The exact eigenvalues and eigenfunctions are obtained. The quantum mechanics of a particle moving…
We investigate numerically the behaviour of damage spreading in a Kauffman cellular automaton with quenched rules on a dynamical $\phi^3$ graph, which is equivalent to coupling the model to discretized 2D gravity. The model is interesting…
We study qualitative properties of two-dimensional freezing cellular automata with a binary state set initialized on a random configuration. If the automaton is also monotone, the setting is equivalent to bootstrap percolation. We explore…
We propose a 2-dimensional cellular automaton model to simulate pedestrian traffic. It is a vmax=1 model with exclusion statistics and parallel dynamics. Long-range interactions between the pedestrians are mediated by a so called floor…
Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of…
We introduce density dependence of the cell size in cellular-automaton models for traffic flow, which allows a more precise correspondence between real-world phenomena and what observed in simulation. Also, we give an explicit calibration…
We define quantum cellular automata as infinite quantum lattice systems with discrete time dynamics, such that the time step commutes with lattice translations and has strictly finite propagation speed. In contrast to earlier definitions…
A universal map is derived for all deterministic 1D cellular automata (CA) containing no freely adjustable parameters. The map can be extended to an arbitrary number of dimensions and topologies and its invariances allow to classify all CA…