Generating irregular fractals based on iterated function systems

• Published in: AIMS mathematics Vol. 9; no. 5; pp. 13346 - 13357
• Main Authors: Zhang, Baoxing, Zhang, Yunkun, Xie, Yuanyuan
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2024
• Subjects: fractal; iterated function system; local control; multiple function system; subdivision
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2024651

The iterated function system (IFS) is important in different fields like image compression. An important feature of such systems is that they can be used to generate fractals. Yet, for the obtained fractals, it is difficult to locally control them to generate new ones with desired structures at specific places. In this paper, we gave an attempt to solve this problem based on a nonuniform multiple function system. For this, we first analyzed the multiple function systems needed in the generation of the final desired fractals. Based on such analysis, the final fractals with desired structures at specific places can be generated using the nonuniform multiple function system. Moreover, these two procedures were summarized into two algorithms for convenience. Examples were also given to illustrate the performance of the nonuniform multiple function system and the two algorithms in this paper.