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Batik has important aesthetic and cultural values, which records and expresses national culture. Their basic graphical pattern comes from imitating object in natural environment that lots of patterns have self-similar. In this paper, we first analyze self-similar characteristic of butterfly pattern Batik and propose an auto-generation algorithm of butterfly pattern based on fractal geometry. The auto-generation algorithm adopts two-dimensional iterated function system (IFS) to construct fractal. First, it generates basis butterfly shape element by functions and it then repeatable iterates the functions until forming a butterfly pattern. Second, it generates butterfly beard to obtain an entire butterfly pattern by functions. Finally, it uses function to iterate the entire butterfly pattern to generate various pattern layouts. The experimental result shows that the algorithm can automatically generate various and beautiful butterfly fractal pattern. Based on the experimental result, we analyze change regularity between generation patterns and function parameters to obtain the most effective range of various function parameter values, which can perfect the proposed algorithm to quickly generate effective patterns. It realizes digital design of butterfly pattern and enriches pattern of Batik.
Yuan et al. (Sat,) studied this question.