A formal language which is simply a set of sequences is composed of some sentences according to certain rules or symbol strings of finite or infinite sets

and formal language theory considers finite descriptions of languages. We are particularly interested in description methods that are easy to understand and use

lead to algorithms for analyzing sequences and are suitable for automated processing. Based on the formal language structure and the grammar rules of regular expressions

an algebraic language systems which can describe L system and iterated function system (IFS) uniformly is proposed by employing algebra. According to the grammar rules generated by the algebraic language systems

Five types of this system production is characterized. Under the algebraic language systems

the DOL system

IFS

condensation IFS

IFSP

and RIFS are mainly described by combining with fractal theory

then fractal attractor is ex?pressed by the regular expression equations of this system

and some examples are given. As examples showed

some fractal graphics can be constructed simply

clearly and efficiently by the language of algebraic system.