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Continuous automaton
About: Continuous automaton is a research topic. Over the lifetime, 947 publications have been published within this topic receiving 17417 citations.
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TL;DR: In this article, it was shown that a variety of deterministic cellular automaton models of highway traffic flow obey a variational principle which states that, for a given car density, the average car flow is a non-decreasing function of time.
Abstract: It is shown that a variety of deterministic cellular automaton models of highway traffic flow obey a variational principle which states that, for a given car density, the average car flow is a non-decreasing function of time. This result is established for systems whose configurations exhibits local jams of a given structure. If local jams have a different structure, it is shown that either the variational principle may still apply to systems evolving according to some particular rules, or it could apply under a weaker form to systems whose asymptotic average car flow is a well-defined function of car density. To establish these results it has been necessary to characterize among all number-conserving cellular automaton rules which ones may reasonably be considered as acceptable traffic rules. Various notions such as free-moving phase, perfect and defective tiles, and local jam play an important role in the discussion. Many illustrative examples are given.
1 citations
TL;DR: A sperner’s grid is thought of a finite state system, where in the model the automation graphs of the various states gives rise to different groomable light paths in network.
Abstract: A sperner’s grid is thought of a finite state system, where in the model gives rise to an optimal network through characterization of paths .the automation graphs of the various states gives rise to different groomable light paths in network.
1 citations
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TL;DR: In this paper, the authors consider ten European towns and for each one they have data for time series approx. 40 years long and deduce rules and constraints directly from the data set, solving an inverse problem (in which we have input and output measures and we have to determine a system model).
Abstract: Usually applications of urban growth cellular automata are related to an only one town, with transition rules and constraints a priori defined. This seems to be a severe limits in applications. The paper presented is born to follow a different kind of approach, so to have rules and constraints directly from observed past data. We consider ten European towns and for each one we have data for time series approx. 40 years long. We deduce rules and constraints directly from the data set, solving an inverse problem (in which we have input and output measures and we have to determine a system model).The study aims to define in detail the stochastic or deterministic character of transition rules (in the stochastic case evaluating transition probability). At last the rules are applied to towns maps (by means of ad hoc cellular automaton). With this cellular automaton we try to simulate past dynamics (for a validation of the model) and also to forecast the spatial development of the towns by means of scenarios (based on the past histories of the cities).
1 citations
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TL;DR: A weakly universal cellular automaton with two states only on the tiling {11,3} is constructed and is a true planar one.
Abstract: In this paper, we construct a weakly universal cellular automaton with two states only on the tiling {11,3}. The cellular automaton is rotation invariant and it is a true planar one.
1 citations
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TL;DR: In this article, a new classification of elementary cellular automata is proposed based on the structure of the network of states, connected with the transitions between them; the latter are determined by the automaton rule.
Abstract: We present a new classification of elementary cellular automata. It is based on the structure of the network of states, connected with the transitions between them; the latter are determined by the automaton rule. Recently an algorithm has been proposed to compress the network of states (M. J. Krawczyk, Physica A 390 (2011) 2181). In this algorithm, states are grouped into classes, according to the local symmetry of the network. In the new classification, an automaton is described by the number of classes #(N) as dependent on the system size N. In most cases, the results reflect the known classification into 88 groups. However, the function #(N) also appears to be the same for some rules which have not been grouped together yet. In this way, the automaton 23 is equivalent to 232, 77 to 178, 105 to 150, the pair (43, 113) to the pair (142, 212) and the group (12, 68, 207, 221) to the group (34, 48, 187, 243). Furthermore, automata 51, 204, the pair (15, 85) and the pair (170,240) are all mutually equivalent. Results are also presented on the structure of networks of states.
1 citations