A non-logarithmic approach to the rate of convergence of the deterministic chaos game
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917499857010688 |
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| author | Caban, Krzysztof Strobin, Filip |
| author_facet | Caban, Krzysztof Strobin, Filip |
| contents | The aim of this paper is to provide a different perspective in the study of the rate of convergence of the chaos game algorithm to the attractor of an iterated function system. We prove that for any function $ψ$ with $\lim\limits_{\ve\to 0}ψ(\ve)=\infty$, a typical (in the sense of the Baire category) driver yields a rate of recovery comparable to $ψ$. This result extends the main theorem from Leśniak et al. (Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 157, 2024). Moreover, thanks to the change of perspective, we are able to prove that a typical driver gives arbitrarily slow rate of recovery. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15830 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A non-logarithmic approach to the rate of convergence of the deterministic chaos game Caban, Krzysztof Strobin, Filip Dynamical Systems 28A80, 37H12 The aim of this paper is to provide a different perspective in the study of the rate of convergence of the chaos game algorithm to the attractor of an iterated function system. We prove that for any function $ψ$ with $\lim\limits_{\ve\to 0}ψ(\ve)=\infty$, a typical (in the sense of the Baire category) driver yields a rate of recovery comparable to $ψ$. This result extends the main theorem from Leśniak et al. (Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 157, 2024). Moreover, thanks to the change of perspective, we are able to prove that a typical driver gives arbitrarily slow rate of recovery. |
| title | A non-logarithmic approach to the rate of convergence of the deterministic chaos game |
| topic | Dynamical Systems 28A80, 37H12 |
| url | https://arxiv.org/abs/2605.15830 |