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Register a new userTheory and Applications of Two-dimensional, Null-boundary, Nine-Neighborhood, Cellular Automata Linear rules
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Added by
Sudhakar Sahoo
Publication date
2008
fields
Informatics Engineering
and research's language is
English
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This paper deals with the theory and application of 2-Dimensional, nine-neighborhood, null- boundary, uniform as well as hybrid Cellular Automata (2D CA) linear rules in image processing. These rules are classified into nine groups depending upon the number of neighboring cells influences the cell under consideration. All the Uniform rules have been found to be rendering multiple copies of a given image depending on the groups to which they belong where as Hybrid rules are also shown to be characterizing the phenomena of zooming in, zooming out, thickening and thinning of a given image. Further, using hybrid CA rules a new searching algorithm is developed called Sweepers algorithm which is found to be applicable to simulate many inter disciplinary research areas like migration of organisms towards a single point destination, Single Attractor and Multiple Attractor Cellular Automata Theory, Pattern Classification and Clustering Problem, Image compression, Encryption and Decryption problems, Density Classification problem etc.
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In this paper, we analyze the algebraic structure of some null boundary as well as some periodic boundary 2-D Cellular Automata (CA) rules by introducing a new matrix multiplication operation using only AND, OR instead of most commonly used AND, EX-OR. This class includes any CA whose rule, when written as an algebra, is a finite Abelean cyclic group in case of periodic boundary and a finite commutative cyclic monoid in case of null boundary CA respectively. The concept of 1-D Multiple Attractor Cellular Automata (MACA) is extended to 2-D. Using the family of 2-D MACA and the finite Abelian cyclic group, an efficient encompression algorithm is proposed for binary images.
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes a bounded number of state changes in any orbit, and finally cellular automata where each orbit converges to some fixed point. Many examples studied in the literature fit into these definitions, in particular the works on cristal growth started by S. Ulam in the 60s. The central question addressed here is how the computational power and computational hardness of basic properties is affected by the constraints of convergence, bounded number of change, or local decreasing of states in each cell. By studying various benchmark problems (short-term prediction, long term reachability, limits) and considering various complexity measures and scales (LOGSPACE vs. PTIME, communication complexity, Turing computability and arithmetical hierarchy) we give a rich and nuanced answer: the overall computational complexity of such cellular automata depends on the class considered (among the three above), the dimension, and the precise problem studied. In particular, we show that all settings can achieve universality in the sense of Blondel-Delvenne-Kr{u}rka, although short term predictability varies from NLOGSPACE to P-complete. Besides, the computability of limit configurations starting from computable initial configurations separates bounded-change from convergent cellular automata in dimension 1, but also dimension 1 versus higher dimensions for freezing cellular automata. Another surprising dimension-sensitive result obtained is that nilpotency becomes decidable in dimension 1 for all the three classes, while it stays undecidable even for freezing cellular automata in higher dimension.
In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at 0. Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are defined as linear numbers and the properties of these linear numbers are studied.
Two-dimensional nine neighbor hood rectangular Cellular Automata rules can be modeled using many different techniques like Rule matrices, State Transition Diagrams, Boolean functions, Algebraic Normal Form etc. In this paper, a new model is introduced using color graphs to model all the 512 linear rules. The graph theoretic properties therefore studied in this paper simplifies the analysis of all linear rules in comparison with other ways of its study.
This paper presents a classification of Cellular Automata rules based on its properties at the nth iteration. Elaborate computer program has been designed to get the nth iteration for arbitrary 1-D or 2-D CA rules. Studies indicate that the figures at some particular iteration might be helpful for some specific application. The hardware circuit implementation can be done using opto-electronic components [1-7].
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