Pith Number

pith:SRL65GQY

pith:2026:SRL65GQY47CZXCKVV6INFTSE5V

not attested not anchored not stored refs resolved

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

Filip Strobin, Krzysztof Caban

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.

arxiv:2605.15830 v1 · 2026-05-15 · math.DS

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\pithnumber{SRL65GQY47CZXCKVV6INFTSE5V}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

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.

C2weakest assumption

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.

C3one line summary

Proves that typical drivers in the chaos game for iterated function systems yield convergence rates comparable to any ψ→∞ and can be arbitrarily slow.

References

12 extracted · 12 resolved · 0 Pith anchors

[1] J. P. Allouche, J. Shallit,Automatic Sequences. Theory, Applications, Generalizations, Cambridge University Press, 2003 2003

[2] V. Becher, P. A. Heiber,On extending de Bruijn sequences, Inform. Process. Lett., 111 (18), pp. 930–932 (2011) 2011

[3] B´ ar´ any, N 2023

[4] P. G. Barrientos, F. H. Ghane, D. Malicet, A. Sarizadeh,On the chaos game of iterated function systems. Topol. Methods Nonlinear Anal. 49(1), 105132 (2017) 2017

[5] M. F. Barnsley,Fractals Everywhere, Academic Press, 1988 1988

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:20.698991Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9457ee9a18e7c59b8955af90d2ce44ed5eb35b743f02da723e10ff349b19a924

Aliases

arxiv: 2605.15830 · arxiv_version: 2605.15830v1 · doi: 10.48550/arxiv.2605.15830 · pith_short_12: SRL65GQY47CZ · pith_short_16: SRL65GQY47CZXCKV · pith_short_8: SRL65GQY

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SRL65GQY47CZXCKVV6INFTSE5V \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 9457ee9a18e7c59b8955af90d2ce44ed5eb35b743f02da723e10ff349b19a924

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f69066309219201b921d5d0a20880061a3b6ef496221ea02ecab75a65ddfc299",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-15T10:31:13Z",
    "title_canon_sha256": "c910279c014414f803fc103a1a235d01c17325b6f9b627a177bc15a5e90a39a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15830",
    "kind": "arxiv",
    "version": 1
  }
}