Abstract: Fabric design is a kind of complex texture pattern, with winding curve, regular and
irregular geometrical patterns as the main pattern. Although the pattern generation methods of
paper-cut design and fractal pattern have a lot of research work, the computer automatic generation
method for fabric design characteristics in Xinjiang still exists many challenging problems.
Considering the difficulties of stylized model building of Xinjiang fabric pattern, the method that uses
pattern symmetry as the key index of pattern generation is proposed, build the variable and invariable
mapping of cyclic group and dihedral group, study the representation of pattern symmetry, prob the
relationship between mapping space of group and symmetric graph using symmetric patterns.
Through the simulation experiment of mapping group, the symmetrical design with chaos attractor is
drawn. Experiments show the generation method can improve the symmetry of pattern and rich the
pattern design of fabric.

Key words: plane symmetry group, pattern generation, iterative