Multiple-Function Systems Based on Regular Subdivision
Self-similar fractals can be generated using subdivision and the subdivision curves/surfaces are actually attractors. Such a connection has been studied between fractals and an extended family of subdivision including stationary and non-stationary schemes. This paper aims to move one step further on...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/11/677 |
| _version_ | 1797465221009244160 |
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| author | Baoxing Zhang Hongchan Zheng Yingwei Chen |
| author_facet | Baoxing Zhang Hongchan Zheng Yingwei Chen |
| author_sort | Baoxing Zhang |
| collection | DOAJ |
| description | Self-similar fractals can be generated using subdivision and the subdivision curves/surfaces are actually attractors. Such a connection has been studied between fractals and an extended family of subdivision including stationary and non-stationary schemes. This paper aims to move one step further on such a connection and introduce multiple-function systems, which has a set of function systems and choose one for each step of iteration. These multiple-function systems can be obtained by deriving the iterated function systems based on the subdivision operators and applying some modifications, including deleting some transformations, to them. Such multiple-function systems can be arranged in a tree structure and can generate different attractors along different paths in the tree. Several examples are presented to illustrate the performance of these multiple-function systems. |
| first_indexed | 2024-03-09T18:19:26Z |
| format | Article |
| id | doaj.art-36895f7dd3f946099ec7408600cc9398 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T18:19:26Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-36895f7dd3f946099ec7408600cc93982023-11-24T08:25:03ZengMDPI AGFractal and Fractional2504-31102022-11-0161167710.3390/fractalfract6110677Multiple-Function Systems Based on Regular SubdivisionBaoxing Zhang0Hongchan Zheng1Yingwei Chen2School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, ChinaSchool of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072, ChinaSchool of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, ChinaSelf-similar fractals can be generated using subdivision and the subdivision curves/surfaces are actually attractors. Such a connection has been studied between fractals and an extended family of subdivision including stationary and non-stationary schemes. This paper aims to move one step further on such a connection and introduce multiple-function systems, which has a set of function systems and choose one for each step of iteration. These multiple-function systems can be obtained by deriving the iterated function systems based on the subdivision operators and applying some modifications, including deleting some transformations, to them. Such multiple-function systems can be arranged in a tree structure and can generate different attractors along different paths in the tree. Several examples are presented to illustrate the performance of these multiple-function systems.https://www.mdpi.com/2504-3110/6/11/677fractalsattractorssubdivisioniterated function systemstrees of function systems |
| spellingShingle | Baoxing Zhang Hongchan Zheng Yingwei Chen Multiple-Function Systems Based on Regular Subdivision Fractal and Fractional fractals attractors subdivision iterated function systems trees of function systems |
| title | Multiple-Function Systems Based on Regular Subdivision |
| title_full | Multiple-Function Systems Based on Regular Subdivision |
| title_fullStr | Multiple-Function Systems Based on Regular Subdivision |
| title_full_unstemmed | Multiple-Function Systems Based on Regular Subdivision |
| title_short | Multiple-Function Systems Based on Regular Subdivision |
| title_sort | multiple function systems based on regular subdivision |
| topic | fractals attractors subdivision iterated function systems trees of function systems |
| url | https://www.mdpi.com/2504-3110/6/11/677 |
| work_keys_str_mv | AT baoxingzhang multiplefunctionsystemsbasedonregularsubdivision AT hongchanzheng multiplefunctionsystemsbasedonregularsubdivision AT yingweichen multiplefunctionsystemsbasedonregularsubdivision |