A computer scientist’s perspective on approximation of IFS invariant sets and measures with the random iteration algorithm
We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which actual numerical computation takes place. In this context, we...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Polish Academy of Sciences
2024-11-01
|
| Series: | International Journal of Electronics and Telecommunications |
| Subjects: | |
| Online Access: | https://journals.pan.pl/Content/133241/PDF/41_4838_Martyn_L_sk.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850266061478297600 |
|---|---|
| author | Tomasz Martyn |
| author_facet | Tomasz Martyn |
| author_sort | Tomasz Martyn |
| collection | DOAJ |
| description | We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which actual numerical computation takes place. In this context, we investigate the possibility of the application of the random iteration algorithm to approximate these discrete IFS invariant sets and measures. The problems concerning a discretization of hyperbolic IFSs are considered as special cases of this more general setting. |
| format | Article |
| id | doaj-art-78936b802e294b91a8cb2abbd5beaee9 |
| institution | OA Journals |
| issn | 2081-8491 2300-1933 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | International Journal of Electronics and Telecommunications |
| spelling | doaj-art-78936b802e294b91a8cb2abbd5beaee92025-08-20T01:54:16ZengPolish Academy of SciencesInternational Journal of Electronics and Telecommunications2081-84912300-19332024-11-01vol. 70No 4https://doi.org/10.24425/ijet.2024.152514A computer scientist’s perspective on approximation of IFS invariant sets and measures with the random iteration algorithmTomasz Martyn0Faculty of Electronics and Information Theory, Warsaw University of Technology, PolandWe study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which actual numerical computation takes place. In this context, we investigate the possibility of the application of the random iteration algorithm to approximate these discrete IFS invariant sets and measures. The problems concerning a discretization of hyperbolic IFSs are considered as special cases of this more general setting.https://journals.pan.pl/Content/133241/PDF/41_4838_Martyn_L_sk.pdfifsdiscrete spacemarkov chainapproximationinvariant setinvariant measure |
| spellingShingle | Tomasz Martyn A computer scientist’s perspective on approximation of IFS invariant sets and measures with the random iteration algorithm International Journal of Electronics and Telecommunications ifs discrete space markov chain approximation invariant set invariant measure |
| title | A computer scientist’s perspective on approximation of IFS invariant sets and measures with the random iteration algorithm |
| title_full | A computer scientist’s perspective on approximation of IFS invariant sets and measures with the random iteration algorithm |
| title_fullStr | A computer scientist’s perspective on approximation of IFS invariant sets and measures with the random iteration algorithm |
| title_full_unstemmed | A computer scientist’s perspective on approximation of IFS invariant sets and measures with the random iteration algorithm |
| title_short | A computer scientist’s perspective on approximation of IFS invariant sets and measures with the random iteration algorithm |
| title_sort | a computer scientist s perspective on approximation of ifs invariant sets and measures with the random iteration algorithm |
| topic | ifs discrete space markov chain approximation invariant set invariant measure |
| url | https://journals.pan.pl/Content/133241/PDF/41_4838_Martyn_L_sk.pdf |
| work_keys_str_mv | AT tomaszmartyn acomputerscientistsperspectiveonapproximationofifsinvariantsetsandmeasureswiththerandomiterationalgorithm |