Determinism in cellular automata - investigation of transition rules

2004 ◽  
Author(s):  
S. Supratid ◽  
R. Sadananda
Keyword(s):  
Cellular Automata ◽  
Transition Rules

On Uniqueness of the Wulff Shape for Cellular Automata

1991 ◽  
Vol 14 (1) ◽  
pp. 75-89
Author(s):  
Paweł Wlaź
Keyword(s):  
Cellular Automata ◽  
Large Class ◽  
Growth Function ◽  
Wulff Shape ◽  
Transition Rules

In this paper, ordered transition rules are investigated. Such rules describe an increment of mono-crystals and for every rule one can calculate so called Wulff Shape. It is shown that for some large class of these rules, there exists at most one growth function which generates a given Wulff Shape.

scholarly journals Integrating Cellular Automata with Unsupervised Deep-Learning Algorithms: A Case Study of Urban-Sprawl Simulation in the Jingjintang Urban Agglomeration, China

2019 ◽  
Vol 11 (9) ◽  
pp. 2464
Author(s):  
Cong Ou ◽  
Jianyu Yang ◽  
Zhenrong Du ◽  
Xin Zhang ◽  
Dehai Zhu
Keyword(s):  
Machine Learning ◽  
Deep Learning ◽  
Cellular Automata ◽  
Urban Sprawl ◽  
Learning Algorithms ◽  
Machine Learning Algorithms ◽  
Urban Agglomeration ◽  
Unsupervised Deep Learning ◽  
Ca Model ◽  
Transition Rules

An effective simulation of the urban sprawl in an urban agglomeration is conducive to making regional policies. Previous studies verified the effectiveness of the cellular-automata (CA) model in simulating urban sprawl, and emphasized that the definition of transition rules is the key to the construction of the CA model. However, existing simulation models based on CA are limited in defining complex transition rules. The aim of this study was to investigate the capability of two unsupervised deep-learning algorithms (deep-belief networks, DBN) and stacked denoising autoencoders (SDA) to define transition rules in order to obtain more accurate simulated results. Choosing the Beijing–Tianjin–Tangshan urban agglomeration as the study area, two proposed models (DBN–CA and SDA–CA) were implemented in this area for simulating its urban sprawl during 2000–2010. Additionally, two traditional machine-learning-based CA models were built for comparative experiments. The implementation results demonstrated that integrating CA with unsupervised deep-learning algorithms is more suitable and accurate than traditional machine-learning algorithms on both the cell level and pattern level. Meanwhile, compared with the DBN–CA, the SDA–CA model had better accuracy in both aspects. Therefore, the unsupervised deep-learning-based CA model, especially SDA–CA, is a novel approach for simulating urban sprawl and also potentially for other complex geographical phenomena.

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.

Urban Expansion Simulation of Southeast England Using Population Surface Modelling and Cellular Automata

10.1068/a3520 ◽  
2002 ◽  
Vol 34 (10) ◽  
pp. 1855-1876 ◽  
Author(s):  
Fulong Wu ◽  
David Martin
Keyword(s):  
Cellular Automata ◽  
Urban Growth ◽  
Urban Expansion ◽  
Empirical Relationship ◽  
Land Development ◽  
Population Projections ◽  
Surface Modelling ◽  
Commuting Time ◽  
Transition Rules ◽  
Proper Balance

The question of where to accommodate future urban expansion has become a politically sensitive issue in many regions. Against the backdrop of ‘urban compaction’ policy, this study uses population surface modelling and cellular automata (CA) to conduct an empirical urban growth simulation for Southeast England. This implementation leads to a consideration of the proper balance between the theoretical abstraction of self-organised growth and empirical constraints to land development. Specifically, we use 1991 and 1997 postcode directories to construct population surfaces. From these, the distributions of developed and vacant (rural) land are derived. Development potential is assessed through accessibility surfaces, which are constructed from the travel/commuting time to major London rail termini, to motorway junctions, and to principal settlements. Through investigating the frequencies of land development in relation to the accessibility surfaces, we can begin to understand the distribution of land development in this region. Based on this empirical relationship, the transition rules of a CA simulation of future urban expansion are constructed. In addition, government population projections at the county level are used to constrain simulation to the year 2020. The study demonstrates the utility of empirical CA in urban growth modelling; in particular the importance of empirically informed CA simulation rules in characterising the distribution of land development.

Validation of Cellular Automata Model of Dynamic Recrystallization

2015 ◽  
Vol 651-653 ◽  
pp. 581-586 ◽  
Author(s):  
Mateusz Sitko ◽  
Łukasz Madej ◽  
Maciej Pietrzyk
Keyword(s):  
Cellular Automata ◽  
Dynamic Recrystallization ◽  
Internal Variables ◽  
Cellular Automata Model ◽  
Proposed Model ◽  
Digital Material ◽  
Ca Model ◽  
Transition Rules ◽  
Development And Validation ◽  
Neighborhood Type

Development and validation of the micro scale cellular automata (CA) model of dynamic recrystallization (DRX) were the main goals of the present paper. Major assumptions of the developed CA DRX model, which is based on the Digital Material Representation (DMR) concept, are described. Parameters like neighborhood type, state and internal variables of the proposed model and their influence on final results are presented and discussed. Particular attention was put on description of the developed transition rules used to replicate mechanisms leading to dynamic recrystallization. Finally, obtained results in the form of flow stress curves are compared with the experimental predictions.

Exploration of Spatial Scale Sensitivity in Geographic Cellular Automata

2005 ◽  
Vol 32 (5) ◽  
pp. 693-714 ◽  
Author(s):  
André Ménard ◽  
Danielle J Marceau
Keyword(s):  
Cellular Automata ◽  
Land Cover ◽  
Spatial Scale ◽  
Data Availability ◽  
Von Neumann ◽  
Geographic Context ◽  
Individual Based Models ◽  
Considerable Impact ◽  
Simulation Results ◽  
Transition Rules

Cellular automata (CA) are individual-based models in which states, time, and space are discrete. Spatiotemporal dynamics emerge from the simple and local interactions of the cells. When using CA in a geographic context, nontrivial questions have to be answered about the choice of spatial scale, namely cell size and neighbourhood configuration. However, the spatial scale decisions involved in the elaboration of geographic cellular automata (GCA) are often made arbitrarily or in relation to data availability. The objective of this study is to evaluate the sensitivity of GCA to spatial scale. A stochastic GCA was built to model land-cover change in the Maskoutains region (Quebec, Canada). The transition rules were empirically derived from two Landsat-TM (30 m resolution) images taken in 1999 and 2002 that have been resampled to four resolutions (100, 200, 500, 1000 m). Six different neighbourhood configurations were considered (Moore, Von Neumann, and circular approximations of 2, 3, 4, and 5 cell radii). Simulations were performed for each of the thirty spatial scale scenarios. Results show that spatial scale has a considerable impact on simulation dynamics in terms of both land-cover area and spatial structure. The spatial scale domains present in the results reveal the nonlinear relationships that link the spatial scale components to the simulation results.

scholarly journals On the semantic security of cellular automata based pseudo-random permutation using results from the Luby-Rackoff construction

2015 ◽  
Vol 15 (1) ◽  
pp. 21
Author(s):  
Kamel Mohammed Faraoun
Keyword(s):  
Cellular Automata ◽  
Block Cipher ◽  
Random Permutation ◽  
Block Ciphers ◽  
Random Permutations ◽  
Semantic Security ◽  
Transition Rules ◽  
Reversible Cellular Automata ◽  
Symmetric Block ◽  
Number Of Iterations

This paper proposes a semantically secure construction of pseudo-random permutations using second-order reversible cellular automata. We show that the proposed construction is equivalent to the Luby-Rackoff model if it is built using non-uniform transition rules, and we prove that the construction is strongly secure if an adequate number of iterations is performed. Moreover, a corresponding symmetric block cipher is constructed and analysed experimentally in comparison with popular ciphers. Obtained results approve robustness and efficacy of the construction, while achieved performances overcome those of some existing block ciphers.

scholarly journals Orbits of the Bernoulli measure in single-transition asynchronous cellular automata

2011 ◽  
Vol DMTCS Proceedings vol. AP,... (Proceedings) ◽  
Author(s):  
Henryk Fukś ◽  
Andrew Skelton
Keyword(s):  
Cellular Automata ◽  
Initial Density ◽  
Response Curves ◽  
Asynchronous Cellular Automata ◽  
Final Density ◽  
Short Cylinder ◽  
Bernoulli Measure ◽  
Single Transition ◽  
International Audience ◽  
Transition Rules

International audience We study iterations of the Bernoulli measure under nearest-neighbour asynchronous binary cellular automata (CA) with a single transition. For these CA, we show that a coarse-level description of the orbit of the Bernoulli measure can be obtained, that is, one can explicitly compute measures of short cylinder sets after arbitrary number of iterations of the CA. In particular, we give expressions for probabilities of ones for all three minimal single-transition rules, as well as expressions for probabilities of blocks of length 3 for some of them. These expressions can be interpreted as "response curves'', that is, curves describing the dependence of the final density of ones on the initial density of ones.

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