Fractal Graphic Algebra Language System Research

During the past decades, fractal graphics have received tremendous attention due to their potential application in computer graphics. L System and Iterative Function System (IFS) are classical in fractal shape generation system, the development of their research in the field of fractal science have a great significance. However, they are generated in the process of their own shortcomings, such as IFS code is difficult to find, the strings of L System is difficult to describe. In order to solve these disadvantages, this paper proposes algebraic language (AL) system.This paper first introduces the historical development of the fractal, the theory of formal languages, the basic theories of fractal and typical methods of generating fractal graphics, such as the L System, Iterative Function System and so on. According to the theory of formal language, we study the basic concepts, operational properties, grammatical structure, regular expressions of AL system. In order to represent fractal graphics more efficiently, based on grammar structure of AL system and grammar rules of regular expressions, we propose AL system of fractal graphics. This system established contacts between the AL system and fractal, set some parameters of the constants, variables, mathematical functions, geometry of the custom character, the number of iterations, axioms and rules. L System and the IFS are described by using a uniform method of AL, this AL system mainly describe the DOL Systems, IFS, iterative function systems with condensed set, stochastic iterative function system(IFSP), and recurrent iterative function system(RIFS), Meanwhile the fractal attractor is expressed by the regular expression equation solution of this system, and fives some examples. The experiment results indicate that the fractal graph could be simply, clearly and efficiently expressed via this language algebraic system.Algebraic language system provides a new method for the theoretical description of the fractal. It greatly reduces the difficulties of the formal description and enhances the ability of the fractal expression. The system can be more limits using L system and IFS advantages, also be used algebraic language algebraic operations, which can generate more complex fractals.