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arXiv · 2605.15830

A non-logarithmic approach to the rate of convergence of the deterministic chaos game

Krzysztof Caban·Filip Strobin
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Abstract

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 $\psi$ with $\lim\limits_{\ve\to 0}\psi(\ve)=\infty$, a typical (in the sense of the Baire category) driver yields a rate of recovery comparable to $\psi$. This result extends the main theorem from Le\'sniak 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.

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Krzysztof Caban, Filip Strobin. 2026-05-15. A non-logarithmic approach to the rate of convergence of the deterministic chaos game. https://arxiv.org/abs/2605.15830

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