The complexity of sequences generated by the arc-fractal system
We study properties of the symbolic sequences extracted from the fractals generated by the arc-fractal system introduced earlier by Huynh and Chew. The sequences consist of only a few symbols yet possess several nontrivial properties. First using an operator approach, we show that the sequences are...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2015
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| Online Access: | https://hdl.handle.net/10356/107025 http://hdl.handle.net/10220/25247 |
| _version_ | 1826116201952051200 |
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| author | Huynh, Hoai Nguyen Pradana, Andri Chew, Lock Yue |
| author2 | Hernandez Montoya, Alejandro Raul |
| author_facet | Hernandez Montoya, Alejandro Raul Huynh, Hoai Nguyen Pradana, Andri Chew, Lock Yue |
| author_sort | Huynh, Hoai Nguyen |
| collection | NTU |
| description | We study properties of the symbolic sequences extracted from the fractals generated by the arc-fractal system introduced earlier by Huynh and Chew. The sequences consist of only a few symbols yet possess several nontrivial properties. First using an operator approach, we show that the sequences are not periodic, even though they are constructed from very simple rules. Second by employing the ϵ-machine approach developed by Crutchfield and Young, we measure the complexity and randomness of the sequences and show that they are indeed complex, i.e. neither periodic nor random, with the value of complexity measure being significant as compared to the known example of logistic map at the edge of chaos. The complexity and randomness of the sequences are then discussed in relation with the properties of associated fractal objects, such as their fractal dimension, symmetry and orientations of the arcs. |
| first_indexed | 2024-10-01T04:07:28Z |
| format | Journal Article |
| id | ntu-10356/107025 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:07:28Z |
| publishDate | 2015 |
| record_format | dspace |
| spelling | ntu-10356/1070252023-02-28T19:21:16Z The complexity of sequences generated by the arc-fractal system Huynh, Hoai Nguyen Pradana, Andri Chew, Lock Yue Hernandez Montoya, Alejandro Raul School of Physical and Mathematical Sciences Complexity Institute DRNTU::Science::Chemistry::Physical chemistry::Molecular structure and bonding We study properties of the symbolic sequences extracted from the fractals generated by the arc-fractal system introduced earlier by Huynh and Chew. The sequences consist of only a few symbols yet possess several nontrivial properties. First using an operator approach, we show that the sequences are not periodic, even though they are constructed from very simple rules. Second by employing the ϵ-machine approach developed by Crutchfield and Young, we measure the complexity and randomness of the sequences and show that they are indeed complex, i.e. neither periodic nor random, with the value of complexity measure being significant as compared to the known example of logistic map at the edge of chaos. The complexity and randomness of the sequences are then discussed in relation with the properties of associated fractal objects, such as their fractal dimension, symmetry and orientations of the arcs. Published version 2015-03-18T01:20:00Z 2019-12-06T22:23:23Z 2015-03-18T01:20:00Z 2019-12-06T22:23:23Z 2015 2015 Journal Article Huynh, H. N., Pradana, A., & Chew, L. Y. (2015). The complexity of sequences generated by the arc-fractal system. PLOS One, 10(2), e0117365-. 1932-6203 https://hdl.handle.net/10356/107025 http://hdl.handle.net/10220/25247 10.1371/journal.pone.0117365 25700034 en PLOS One © 2015 Huynh et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. 21 p. application/pdf |
| spellingShingle | DRNTU::Science::Chemistry::Physical chemistry::Molecular structure and bonding Huynh, Hoai Nguyen Pradana, Andri Chew, Lock Yue The complexity of sequences generated by the arc-fractal system |
| title | The complexity of sequences generated by the arc-fractal system |
| title_full | The complexity of sequences generated by the arc-fractal system |
| title_fullStr | The complexity of sequences generated by the arc-fractal system |
| title_full_unstemmed | The complexity of sequences generated by the arc-fractal system |
| title_short | The complexity of sequences generated by the arc-fractal system |
| title_sort | complexity of sequences generated by the arc fractal system |
| topic | DRNTU::Science::Chemistry::Physical chemistry::Molecular structure and bonding |
| url | https://hdl.handle.net/10356/107025 http://hdl.handle.net/10220/25247 |
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