{"paper":{"title":"A non-logarithmic approach to the rate of convergence of the deterministic chaos game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"For any function diverging to infinity at zero, a typical driver gives chaos game recovery rate comparable to that function, and typical drivers converge arbitrarily slowly.","cross_cats":[],"primary_cat":"math.DS","authors_text":"Filip Strobin, Krzysztof Caban","submitted_at":"2026-05-15T10:31:13Z","abstract_excerpt":"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 arbitraril"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For any function ψ with lim ε→0 ψ(ε)=∞, a typical (Baire category) driver yields a rate of recovery comparable to ψ. Moreover, a typical driver gives arbitrarily slow rate of recovery.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The IFS consists of contractions on a complete metric space and the 'driver' is a sequence in the symbol space such that the Baire category topology on the space of drivers is well-defined and the rate of recovery is measured via the distance to the attractor after n steps.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves that typical drivers in the chaos game for iterated function systems yield convergence rates comparable to any ψ→∞ and can be arbitrarily slow.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"For any function diverging to infinity at zero, a typical driver gives chaos game recovery rate comparable to that function, and typical drivers converge arbitrarily slowly.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b350fedb50f6f49acd4dc94614d81f8984e95671db5d8c404f057a828bd59e41"},"source":{"id":"2605.15830","kind":"arxiv","version":1},"verdict":{"id":"293701cf-f966-4602-8c9b-d7a5f6666070","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:24:52.828186Z","strongest_claim":"For any function ψ with lim ε→0 ψ(ε)=∞, a typical (Baire category) driver yields a rate of recovery comparable to ψ. 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