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The Symbol Method Of Iteration Function System

Posted on:2011-10-06Degree:MasterType:Thesis
Country:ChinaCandidate:C Y WangFull Text:PDF
GTID:2178360305490698Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
More and more people are concerned about fractal graphics which is an important content of computer graphics. Iterated function system and L-system are two classical mathematical system of constructing fractal image and their continuous development have great significance to the whole field of fractal. In order to study the relationship between different IFS, the definition and operating properties of IFS addition,direct product, compound product and similar that have obvious geometric and algebraic meaning are researched, based on the theory of IFS attractor generating. It is helpful for recognizing the relations of some IFS attractor, and constructing more fractals to simulate natural objects based on known IFS by means of defining various mathematical operations of IFS firstly in this paper. Then by way of analyzing process of generating fractal graphics with deterministic algorithm, the definition of symbol system is given based on symbolic IFS; To be able to quickly and easily implement some classical fractals a small number of predefined symbols is retained. Users can set up several custom symbols with parameter, which represent constant, variable, mathematical function, give axiom, rules, and the number of iteration, then the system will automatically generate user-defined fractal; Generating algorithm of symbol system is proposed and its explanation program is analyzed; Through establishing the correspond relationship between n hexadecimal numbers and the change, the algorithm is improved to some extent, the time complexity and space complexity is reduced. Symbol system can describe and process various types of IFS, L-system, mid-point displacement cure using a uniform method, and enhance the ability of expressing fractal graphics. Special fractal graphic which is achieved with different methods can achieved in symbol system. Efficient generating algorithm also could be applied in symbol system. Say in other words, it retains advantage of original system. Symbol system is expressed with document format, readable, easy to understand and algorithm is fast, efficient. Initial set no longer confined to the set or image, and if initial set is selected appropriate generating speed can be improved.
Keywords/Search Tags:fractal, iterated function system, L-system, symbolic system, attractor
PDF Full Text Request
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