为了更高效地表示分形图形,依据形式语言的文法结构及正则表达式的文法规则,通过引入代数运算,提出一个能够对L系统和迭代函数系统(IFS)统一描述的语言代数系统.根据语言代数系统产生式的文法规则,将此系统的产生式集划分为5类.结合分形理论,此语言代数系统着重将DOL系统、迭代函数系统(IFS)、带凝聚集迭代函数系统(凝聚IFS)、随机迭代函数系统(IFSP)和再归迭代函数系统(RIFS)等进行描述,同时用此系统的正则表达式方程解将分形吸引子进行代数表示,并给出一些实例.通过实例表明,分形图形可以用该语言代数系统简单、明了、高效地表示.%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 express fractal graph more efficiently, according to the grammatical structure of formal language and the grammatical rules of regular expressions , through the introduction of algebra operations, a language algebraic system which can uniformly describe L-system and iterative function system ( IFS) is proposed. According to the grammatical rules of language algebra system, the producing types are divided into five categories. Combining the fractal theory, this language algebraic system mainly describe L-system, iterative function system (IFS) ,iteration function system with condensed set, stochastic iteration 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 gives some examples. The experiment results indicate that the fractal graph could be simply, clearly and efficiently expressed via this language algebraic system.
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