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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Lucian Law Determines Feigenbaum Universality - A Synthesis of Three Results

Authors: Randolph, Lucian;

Lucian Law Determines Feigenbaum Universality - A Synthesis of Three Results

Abstract

Description/Abstract: We show that Feigenbaum universality—the appearance of the constants δ = 4.669... and α = 2.502... across all period-doubling cascades—is not a foundational principle but a consequence of a deeper geometric law. The Lucian Law states that bounded nonlinear systems with coupling necessarily produce fractal geometry. Three papers, taken together, establish a closed logical chain: (1) the Lucian Law generates the Feigenbaum constants through the geometry of the cascade, (2) the Feigenbaum constants structure the Lucian Law’s own prerequisites through the decay bounce mechanism, and (3) the loop closes—the Law is self-grounding. This note synthesizes the argument and establishes the four-layer universality hierarchy. Keywords: Feigenbaum universality, period-doubling cascade, renormalization, self-grounding, fractal geometry, Lucian Law

Keywords

Lucian Law, period-doubling cascade, self-grounding, Feigenbaum universality, fractal geometry, renormalization

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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