Abstract
Fractal geometry is a new branch of mathematics, which has a very wide and important application in everyday life. Iterated function systems (abbrev: IFS ) play an important role in constructing fractal set, which is a critical method in fractal geometry. The attractor is also an important concept of fractal geometry, which is obtained by an iterated function systems or a super iterated function systems (abbrev: SIFS). The SIFS is a significant generalization of the IFS by taking the number of functions of the IFS from finity to infinity. This study extend IFS to SIFS through uniform convergence. Then, some important properties similar to IFS are obtained, particularly the property of the attractors. Finally, The relationship among the attractors between SIFS and IFS is obtained, denoted by .
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