COLLATZ FRACTAL PATTERNS - RECORD HOLDERS ANALYSIS

I've discovered a novel fractal structure in the record-breaking numbers of the Collatz conjecture. The differences between successive record holders exhibit reversible cycles and a self-similar hierarchical pattern across multiple scales, from small integers to numbers with over 24 digits. These findings suggest an unexpected internal hierarchy in the growth of Collatz record holders and offer a promising heuristic to predict future records without exhaustive computation.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-08-07
DOI
https://doi.org/10.5281/zenodo.16756779
Primary Topic
Benford’s Law and Fraud Detection
Type
article
Field-Weighted Citation Impact
0.00
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article

COLLATZ FRACTAL PATTERNS - RECORD HOLDERS ANALYSIS

Zenodo (CERN European Organization for Nuclear Research)
Benford’s Law and Fraud Detection
article

COLLATZ FRACTAL PATTERNS - RECORD HOLDERS ANALYSIS

article en

Abstract

I've discovered a novel fractal structure in the record-breaking numbers of the Collatz conjecture. The differences between successive record holders exhibit reversible cycles and a self-similar hierarchical pattern across multiple scales, from small integers to numbers with over 24 digits. These findings suggest an unexpected internal hierarchy in the growth of Collatz record holders and offer a promising heuristic to predict future records without exhaustive computation.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 49%
Benford’s Law and Fraud Detection
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COLLATZ FRACTAL PATTERNS - RECORD HOLDERS ANALYSIS · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS