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Golden Ratio as Invariant of Fractality, Self-Similarity and Recursion

Золотое сечение как инвариант фрактальности, самоподобия и рекурсии

Anton Pankratov(independent)·
phigolden ratiofractalityself-similarityrecursion

Abstract

Abstract

EN

Phi as fixed point of self-referential map f(x)=1+1/x. Discrete iterative invariant complementary to continuous phase invariant pi.

Аннотация

RU

Phi как неподвижная точка самореферентного отображения f(x)=1+1/x. Дискретный итеративный инвариант, комплементарный непрерывному фазовому инварианту pi.

摘要

ZH

Golden ratio and fractality

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Subjects & Identifiers

Subjects:
Mathematical Physics (math-ph) · phi · golden ratio · fractality · self-similarity · recursion
Category:
Mathematical Structures
Authors:
Anton Pankratov (independent researcher)
Submitted:
Last modified:
Languages:
Russian (primary), English
Permanent URL:
https://odtoe.org/en/articles/phi-fractality
Journal:
Observer-Dependent Theory of Everything (ODTOE Corpus)
Comments:
For research collaboration or corrections, contact via /contact. Citations and academic engagement welcome.

Cite this article

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Plain text

APA-like
Pankratov A. "Golden Ratio as Invariant of Fractality, Self-Similarity and Recursion." Observer-Dependent Theory of Everything, odtoe.org, 2026. https://odtoe.org/en/articles/phi-fractality
BibTeX[ click to expand ]
@article{pankratov2026phiFractality,
  author    = {Pankratov, Anton},
  title     = {Golden Ratio as Invariant of Fractality, Self-Similarity and Recursion},
  journal   = {Observer-Dependent Theory of Everything},
  year      = {2026},
  month     = {Feb},
  url       = {https://odtoe.org/en/articles/phi-fractality},
  publisher = {odtoe.org}
}
RIS (EndNote / Reference Manager)[ click to expand ]
TY  - JOUR
AU  - Pankratov, Anton
TI  - Golden Ratio as Invariant of Fractality, Self-Similarity and Recursion
JO  - Observer-Dependent Theory of Everything
PY  - 2026
DA  - 2026-02-13
UR  - https://odtoe.org/en/articles/phi-fractality
PB  - odtoe.org
ER  -
Golden Ratio as Invariant of Fractality, Self-Similarity and RecursionEN

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