Transition Rule Elicitation Methods for Urban Cellular Automata Models

2006 ◽  
pp. 53-68 ◽  
Author(s):  
Junfeng Jiao ◽  
Luc Boerboom
Keyword(s):  
Cellular Automata ◽  
Transition Rule ◽  
Elicitation Methods

Making (Bio)Logical Connections

2018 ◽  
Author(s):  
Subrata Dasgupta
Keyword(s):  
Cellular Automata ◽  
Universal Theory ◽  
Transition Rule ◽  
Yale University ◽  
Von Neumann ◽  
Finite Set ◽  
A Cell ◽  
The 1960S ◽  
The University ◽  
The Brain

At first blush, computing and biology seem an odd couple, yet they formed a liaison of sorts from the very first years of the electronic digital computer. Following a seminal paper published in 1943 by neurophysiologist Warren McCulloch and mathematical logician Warren Pitts on a mathematical model of neuronal activity, John von Neumann of the Institute of Advanced Study, Princeton, presented at a symposium in 1948 a paper that compared the behaviors of computer circuits and neuronal circuits in the brain. The resulting publication was the fountainhead of what came to be called cellular automata in the 1960s. Von Neumann’s insight was the parallel between the abstraction of biological neurons (nerve cells) as natural binary (on–off) switches and the abstraction of physical computer circuit elements (at the time, relays and vacuum tubes) as artificial binary switches. His ambition was to unify the two and construct a formal universal theory. One remarkable aspect of von Neumann’s program was inspired by the biology: His universal automata must be able to self-reproduce. So his neuron-like automata must be both computational and constructive. In 1955, invited by Yale University to deliver the Silliman Lectures for 1956, von Neumann chose as his topic the relationship between the computer and the brain. He died before being able to deliver the lectures, but the unfinished manuscript was published by Yale University Press under the title The Computer and the Brain (1958). Von Neumann’s definitive writings on self-reproducing cellular automata, edited by his one-time collaborator Arthur Burks of the University of Michigan, was eventually published in 1966 as the book Theory of Self-Reproducing Automata. A possible structure of a von Neumann–style cellular automaton is depicted in Figure 7.1. It comprises a (finite or infinite) configuration of cells in which a cell can be in one of a finite set of states. The state of a cell at any time t is determined by its own state and those of its immediate neighbors in the preceding point of time t – 1, according to a state transition rule.

scholarly journals A Cellular Automata Model Constrained by Spatiotemporal Heterogeneity of the Urban Development Strategy for Simulating Land-use Change: A Case Study in Nanjing City, China

2019 ◽  
Vol 11 (15) ◽  
pp. 4012 ◽  
Author(s):  
Jing Yang ◽  
Feng Shi ◽  
Yizhong Sun ◽  
Jie Zhu
Keyword(s):  
Land Use ◽  
Cellular Automata ◽  
Urban Development ◽  
Development Strategy ◽  
Spatial Layout ◽  
Transition Rule ◽  
External Interference ◽  
Nanjing City ◽  
Spatiotemporal Heterogeneity

While cellular automata (CA) has become increasingly popular in land-use and land-cover change (LUCC) simulations, insufficient research has considered the spatiotemporal heterogeneity of urban development strategies and applied it to constrain CA models. Consequently, we proposed to add a zoning transition rule and planning influence that consists of a development grade coefficient and traffic facility coefficient in the CA model to reflect the top-down and heterogeneous characteristics of spatial layout and the dynamic and heterogeneous external interference of traffic facilities on land-use development. Testing the method using Nanjing city as a case study, we show that the optimal combinations of development grade coefficients are different in different districts, and the simulation accuracies are improved by adding the grade coefficients into the model. Moreover, the integration of the traffic facility coefficient does not improve the model accuracy as expected because the deployment of the optimal spatial layout has considered the effect of the subway on land use. Therefore, spatial layout planning is important for urban green, humanistic and sustainable development.

PARALLELIZING THREE DIMENSIONAL CELLULAR AUTOMATA WITH OpenMP

2007 ◽  
Vol 17 (04) ◽  
pp. 349-361
Author(s):  
SANTIAGO GARCIA CARBAJAL
Keyword(s):  
Cellular Automata ◽  
Three Dimensional ◽  
Computing System ◽  
Massively Parallel ◽  
Transition Rule ◽  
Two Dimensional ◽  
Decomposition Procedure ◽  
Massively Parallel Computing ◽  
Transition Rules ◽  
Do So

This paper describes our research on using Genetic Programming to obtain transition rules for Cellular Automata, which are one type of massively parallel computing system. Our purpose is to determine the existence of a limit of chaos for three dimensional Cellular Automata, empirically demonstrated for the two dimensional case. To do so, we must study statistical properties of 3D Cellular Automata over long simulation periods. When dealing with big three dimensional meshes, applying the transition rule to the whole structure can become a extremely slow task. In this work we decompose the Automata into pieces and use OpenMp to parallelize the process. Results show that using a decomposition procedure, and distributing the mesh between a set of processors, 3D Cellular Automata can be studied without having long execution times.

2D Triangular von Neumann Cellular Automata with Periodic Boundary

2019 ◽  
Vol 29 (03) ◽  
pp. 1950029
Author(s):  
Selman Uguz ◽  
Ecem Acar ◽  
Shovkat Redjepov
Keyword(s):  
Cellular Automata ◽  
Periodic Boundary ◽  
Discrete Dynamical System ◽  
Real Life ◽  
Theoretical Biology ◽  
Continuous System ◽  
Transition Rule ◽  
Von Neumann ◽  
Special Cases ◽  
Ternary Field

Cellular automata (CA) theory is a very rich and useful model of a discrete dynamical system that focuses on their local information relying on the neighboring cells to produce CA global behaviors. Although the main structure of CA is a discrete special model, the global behaviors at many iterative times and on big scales can be close to nearly a continuous system. The mathematical points of the basic model imply the computable values of the mathematical structure of CA. After modeling the CA structure, an important problem is to be able to move forwards and backwards on CA to understand their behaviors in more elegant ways. This happens in the possible case if CA is a reversible one. In this paper, we investigate the structure and the reversibility cases of two-dimensional (2D) finite, linear, and triangular von Neumann CA with periodic boundary case. It is considered on ternary field [Formula: see text] (i.e. 3-state). We obtain the transition rule matrices for each special case. It is known that the reversibility cases of 2D CA is generally a very challenging problem. For given special triangular information (transition) rule matrices, we prove which triangular linear 2D von Neumann CA is reversible or not. In other words, the reversibility problem of 2D triangular, linear von Neumann CA with periodic boundary is resolved completely over ternary field. However, the general transition rule matrices are also presented to establish the reversibility cases of these special 3-states CA. Since the main CA structures are sufficiently simple to investigate in mathematical ways and also very complex for obtaining chaotic models, we believe that these new types of CA can be found in many different real life applications in special cases e.g. mathematical modeling, theoretical biology and chemistry, DNA research, image science, textile design, etc. in the near future.

IDENTIFICATION OF THE BELOUSOV–ZHABOTINSKII REACTION USING CELLULAR AUTOMATA MODELS

2007 ◽  
Vol 17 (05) ◽  
pp. 1687-1701 ◽  
Author(s):  
Y. ZHAO ◽  
S. A. BILLINGS ◽  
ALEXANDER F. ROUTH
Keyword(s):  
Experimental Data ◽  
Cellular Automata ◽  
Transition Rule ◽  
New Techniques ◽  
Bz Reaction ◽  
New Methods ◽  
Color Calibration ◽  
Ca Model ◽  
Set Up ◽  
Belousov Zhabotinskii Reaction

New methods of identifying the transition rule of a Belousov–Zhabotinskii (BZ) reaction directly from experimental data using cellular automata (CA) models are investigated. The experimental set-up and new techniques for image pre-processing to ensure the identification of representative models are discussed including noise reduction, pixel and color calibration. Two kinds of models, the Greenberg–Hasting model (GHM) and the polynomial CA model are studied in detail. It is shown that the results of identifying a real BZ reacting system are very encouraging and the predicted patterns compare well with the imaged patterns both visually and quantitatively.

Structure and Reversibility of 2D von Neumann Cellular Automata Over Triangular Lattice

2017 ◽  
Vol 27 (06) ◽  
pp. 1750083 ◽  
Author(s):  
Selman Uguz ◽  
Shovkat Redjepov ◽  
Ecem Acar ◽  
Hasan Akin
Keyword(s):  
Cellular Automata ◽  
Triangular Lattice ◽  
Mathematical Structure ◽  
Continuous Model ◽  
Transition Rule ◽  
Von Neumann ◽  
Basic Model ◽  
Boundary Case ◽  
Ternary Field ◽  
Finite Linear

Even though the fundamental main structure of cellular automata (CA) is a discrete special model, the global behaviors at many iterative times and on big scales could be a close, nearly a continuous, model system. CA theory is a very rich and useful phenomena of dynamical model that focuses on the local information being relayed to the neighboring cells to produce CA global behaviors. The mathematical points of the basic model imply the computable values of the mathematical structure of CA. After modeling the CA structure, an important problem is to be able to move forwards and backwards on CA to understand their behaviors in more elegant ways. A possible case is when CA is to be a reversible one. In this paper, we investigate the structure and the reversibility of two-dimensional (2D) finite, linear, triangular von Neumann CA with null boundary case. It is considered on ternary field [Formula: see text] (i.e. 3-state). We obtain their transition rule matrices for each special case. For given special triangular information (transition) rule matrices, we prove which triangular linear 2D von Neumann CAs are reversible or not. It is known that the reversibility cases of 2D CA are generally a much challenged problem. In the present study, the reversibility problem of 2D triangular, linear von Neumann CA with null boundary is resolved completely over ternary field. As far as we know, there is no structure and reversibility study of von Neumann 2D linear CA on triangular lattice in the literature. Due to the main CA structures being sufficiently simple to investigate in mathematical ways, and also very complex to obtain in chaotic systems, it is believed that the present construction can be applied to many areas related to these CA using any other transition rules.

Wetlands Change Simulation Using Cellular Automata at Multi-Scales

2012 ◽  
Vol 610-613 ◽  
pp. 3616-3623
Author(s):  
Huan Yu ◽  
Bo Kong ◽  
Shu Qing Zhang ◽  
Xin Pan
Keyword(s):  
Cellular Automata ◽  
Temporal Evolution ◽  
Freshwater Wetlands ◽  
Management Decision ◽  
Transition Rule ◽  
Landscape Index ◽  
Visual Effects ◽  
The Sanjiang Plain ◽  
Wetland Landscape ◽  
Evolution Simulation

Wetlands are extremely valuable natural resources, the simulation of wetland landscape spatial-temporal evolution can reveal the mechanisms and laws of landscape succession, achieve the sustainable landscape use and provide wetland conservation and management decision support. Thesis takes the inland freshwater wetlands in the Sanjiang Plain for experimental region, carries out experiment of wetland landscape changing process simulation using Cellular Automata, results show that visual effects of simulation and prediction are both good, and the total accuracy of points to points are also above 79% under each scale, which verifies the feasibility and effectiveness of wetland landscape spatial-temporal evolution simulation using Cellular Automata; scale has influence on transition rule mining, visual effects and accuracy of simulation results, and statistics of landscape index, then scale effect is obvious during wetland landscape spatial-temporal evolution simulation using Cellular Automata, accuracy and contagion index are both showed as exponential distribution with the scale rising, which provides reference for simulation scale selection.

BUILDING EFFICIENT COMPUTATIONAL CELLULAR AUTOMATA MODELS OF COMPLEX SYSTEMS: BACKGROUND, APPLICATIONS, RESULTS, SOFTWARE, AND PATHOLOGIES

2019 ◽  
Vol 22 (05) ◽  
pp. 1950013 ◽  
Author(s):  
JIŘÍ KROC ◽  
FRANCISCO JIMÉNEZ-MORALES ◽  
J. L. GUISADO ◽  
MARÍA CARMEN LEMOS ◽  
JAKUB TKÁČ
Keyword(s):  
Cellular Automata ◽  
Complex Systems ◽  
Cellular Automaton ◽  
Transition Rule ◽  
Large Variability ◽  
Computational Approaches ◽  
Laser Dynamics ◽  
Flow Diagrams ◽  
Software Codes ◽  
Definition Of

Cellular automaton models of complex systems (CSs) are gaining greater popularity; simultaneously, they have proven the capability to solve real scientific and engineering applications. To enable everybody a quick penetration into the core of this type of modeling, three real applications of cellular automaton models, including selected open source software codes, are studied: laser dynamics, dynamic recrystallization (DRX) and surface catalytic reactions. The paper is written in a way that it enables any researcher to reach the cutting edge knowledge of the design principles of cellular automata (CA) models of the observed phenomena in any scientific field. The whole sequence of design steps is demonstrated: definition of the model using topology and local (transition) rule of a cellular automaton, achieved results, comparison to real experiments, calibration, pathological observations, flow diagrams, software, and discussions. Additionally, the whole paper demonstrates the extreme expressiveness and flexibility of massively parallel computational approaches compared to other computational approaches. The paper consists of the introductory parts that are explaining CSs, self-organization and emergence, entropy, and CA. This allows readers to realize that there is a large variability in definitions and solutions of this class of models.

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