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Record W295275604

Golden Fractal Trees

2007· article· en· W295275604 on OpenAlex
T. D. TAYLOR

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

Venuenot available
Typearticle
Languageen
FieldPhysics and Astronomy
TopicAdvanced Mathematical Theories and Applications
Canadian institutionsSt. Francis Xavier University
Fundersnot available
KeywordsGolden ratioFractalKoch snowflakeCantor setMathematicsCombinatoricsGeometryMathematical analysis
DOInot available

Abstract

fetched live from OpenAlex

The famed golden ratio appears in many different forms of art. Historically there have been people who believe that the golden ratio can be used to create the most aesthetically pleasing figures. More recently, fractals have been used to create beautifully intricate art. In this paper, we present an interesting connection between the golden ratio and fractal trees. Four special self-contacting fractal trees that scale with the golden ratio possess remarkable symmetries and provide new visual representations of well-known results involving the golden ratio. Golden variations of familiar fractals including the Cantor set and the Koch curve appear as subsets of golden trees.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.963
Threshold uncertainty score0.999

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0020.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.009
GPT teacher head0.287
Teacher spread0.278 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it