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.

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 Land Use Land Cover map segmentation using Remote Sensing: A Case study of Ajoy river watershed, India

2020 ◽  
Vol 30 (1) ◽  
pp. 273-286
Author(s):  
Kalyan Mahata ◽  
Rajib Das ◽  
Subhasish Das ◽  
Anasua Sarkar
Keyword(s):  
Land Use ◽  
Image Segmentation ◽  
Cellular Automata ◽  
Land Cover ◽  
Satellite Imagery ◽  
Current Model ◽  
Discrete Dynamical System ◽  
Land Use Land Cover ◽  
Data Set ◽  
Validity Indices

Abstract Image segmentation in land cover regions which are overlapping in satellite imagery, is one crucial challenge. To detect true belonging of one pixel becomes a challenging problem while classifying mixed pixels in overlapping regions. In current work, we propose one new approach for image segmentation using a hybrid algorithm of K-Means and Cellular Automata algorithms. This newly implemented unsupervised model can detect cluster groups using hybrid 2-Dimensional Cellular-Automata model based on K-Means segmentation approach. This approach detects different land use land cover areas in satellite imagery by existing K-Means algorithm. Since it is a discrete dynamical system, cellular automaton realizes uniform interconnecting cells containing states. In the second stage of current model, we experiment with a 2-dimensional cellular automata to rank allocations of pixels among different land-cover regions. The method is experimented on the watershed area of Ajoy river (India) and Salinas (California) data set with true class labels using two internal and four external validity indices. The segmented areas are then compared with existing FCM, DBSCAN and K-Means methods and verified with the ground truth. The statistical analysis results also show the superiority of the new method.

scholarly journals Three-state von Neumann cellular automata and pattern generation

2015 ◽  
Vol 39 (7) ◽  
pp. 2003-2024 ◽  
Author(s):  
Ugur Sahin ◽  
Selman Uguz ◽  
Hasan Akın ◽  
Irfan Siap
Keyword(s):  
Cellular Automata ◽  
Pattern Generation ◽  
Von Neumann

scholarly journals Predicting Land use and land cover spatiotemporal changes utilizing CA-Markov model in Duhok district between 1999 and 2033

2020 ◽  
Author(s):  
shamal
Keyword(s):  
Remote Sensing ◽  
Land Use ◽  
Cellular Automata ◽  
Land Cover ◽  
Markov Model ◽  
Markov Chain Model ◽  
United States Geological Survey ◽  
Chain Model ◽  
Lulc Changes ◽  
Spatiotemporal Changes

AbstractTHE PROCESS OF SPATIOTEMPORAL CHANGES IN LAND USE LAND COVER (LULC) AND PREDICTING THEIR FUTURE CHANGES ARE HIGHLY IMPORTANT FOR LULC MANAGERS. ONE OF THE MOST IMPORTANT CHALLENGES IN LULC STUDIES IS CONSIDERED TO BE THE CREATION OF SIMULATION OF FUTURE CHANGE IN LULC THAT INVOLVE SPATIAL MODELING. THE PURPOSE OF THIS STUDY IS TO USE GIS AND REMOTE SENSING TO CLASSIFY LULC CLASSES IN DUHOK DISTRICT BETWEEN 1999 AND 2018, AND THEIR RESULTS CALCULATED USING AN INTEGRATED CELLULAR AUTOMATA AND CA-MARKOV CHAIN MODEL TO SIMULATE LULC CHANGES IN 2033. IN THIS STUDY, SATELLITE IMAGES FROM LANDSAT7 ETM AND LANDSAT8 OLI USED FOR DUHOK DISTRICT WHICH IS LOCATED IN THE NORTHERN PART OF IRAQ OBTAINED FROM UNITED STATES GEOLOGICAL SURVEY (USGS) FOR THE PERIODS (1999 AND 2018) ANALYZED USING REMOTE SENSING AND GIS TECHNIQUES IN ADDITION TO THE GROUND CONTROL POINTS, FOR EACH CLASS 60 GROUND POINTS HAVE TAKEN. TO SIMULATE FUTURE LULC CHANGES FOR 2033, INTEGRATED APPROACHES OF CELLULAR AUTOMATA AND CA-MARKOV MODELS UTILIZED IN IDRISI SELVA SOFTWARE. THE OUTCOMES DEMONSTRATE THAT DUHOK DISTRICT HAS EXPERIENCED A TOTAL OF 184.91KM CHANGES DURING THE PERIOD (TABLE 4). THE PREDICTION ALSO INDICATES THAT THE CHANGES WILL EQUAL TO 235.4 KM BY 2033 (TABLE 8). SOIL AND GRASS CONSTITUTES THE MAJORITY OF CHANGES AMONG LULC CLASSES AND ARE INCREASING CONTINUOUSLY. THE ACHIEVED KAPPA VALUES FOR THE MODEL ACCURACY ASSESSMENT HIGHER THAN 0.93 AND 0.85 FOR 1999 AND 2018 RESPECTIVELY SHOWED THE MODEL’S CAPABILITY TO FORECAST FUTURE LULC CHANGES IN DUHOK DISTRICT. THUS, ANALYZING TRENDS OF LULC CHANGES FROM PAST TO NOW AND PREDICT FUTURE APPLYING CA-MARKOV MODEL CAN PLAY AN IMPORTANT ROLE IN LAND USE PLANNING, POLICY MAKING, AND MANAGING RANDOMLY UTILIZED LULC CLASSES IN THE PROPOSED STUDY AREA

Basic Definitions

2010 ◽  
pp. 17-50
Author(s):  
Eleonora Bilotta ◽  
Pietro Pantano
Keyword(s):  
Cellular Automata ◽  
Dynamic Systems ◽  
Chaotic Behavior ◽  
Crucial Importance ◽  
Von Neumann ◽  
3 Dimensional ◽  
Straight Line ◽  
Discrete Dynamic Systems ◽  
Complex Phenomena ◽  
Emergent Behaviors

Cellular Automata (CAs) are discrete dynamic systems that exhibit chaotic behavior and self-organization and lend themselves to description in rigorous mathematical terms. The main aim of this chapter is to introduce CAs from a formal perspective. Ever since the work of von Neumann (1966), von Neumann & Burks (1970), Toffoli & Norman (1987), Wolfram (1983; 1984), and Langton (1984; 1986; 1990), specialists have recognized CAs as a model of crucial importance for complexity studies. Like other models used in the investigation of complex phenomena (Chua & Yang, 1988; Chua, 1998), a CA consists of a number of elementary components, whose interactions determine its dynamics. In this and the following chapters, we will sometimes refer to these elementary components as cells, sometimes as sites. The cells of a CA can be positioned along a straight line or on a 2 or 3-dimensional grid, creating 1-D, 2-D and 3-D CAs. Automata consisting of cells whose only possible states are 0 or 1, are Boolean Automata; automata whose cells can assume more than 2 states are multi-state CAs. In both cases, the CA contains “elementary particles” whose dynamics are governed by simple rules. These rules determine sometimes unpredictable, emergent behaviors, ranging from the simple, through the complex to the chaotic.

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.

Indian River Watershed Image Analysis Using Fuzzy-CA Hybrid Approach

2017 ◽  
pp. 232-246
Author(s):  
Kalyan Mahata ◽  
Subhasish Das ◽  
Rajib Das ◽  
Anasua Sarkar
Keyword(s):  
Cellular Automata ◽  
Land Cover ◽  
Discrete Dynamical System ◽  
Hybrid Approach ◽  
Ground Truth ◽  
Second Phase ◽  
River Watershed ◽  
Set Membership ◽  
Mixed Pixels ◽  
Indian River

Image segmentation among overlapping land cover areas in satellite images is a very crucial task. Detection of belongingness is the important problem for classifying mixed pixels. This paper proposes an approach for pixel classification using a hybrid approach of Fuzzy C-Means and Cellular automata methods. This new unsupervised method is able to detect clusters using 2-Dimensional Cellular Automata model based on fuzzy segmentations. This approach detects the overlapping regions in remote sensing images by uncertainties using fuzzy set membership values. As a discrete, dynamical system, cellular automaton explores uniformly interconnected cells with states. In the second phase of our method, we utilize a 2-dimensional cellular automata to prioritize allocations of mixed pixels among overlapping land cover areas. We experiment our method on Indian Ajoy river watershed area. The clustered regions are compared with well-known FCM and K-Means methods and also with the ground truth knowledge. The results show the superiority of our new method.

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