{
  "abstract": "The mathematical constants π and e are irrational and transcendental numbers whose infinite, non-repeating decimal expansions mimic randomness. This study investigates potential underlying structures within these sequences by treating their digits as discrete time-series signals. Using Higuchi’s algorithm, we calculate their fractal dimensions to quantify their inherent complexity. Because the efficacy of Higuchi’s method depends heavily on the maximum window size (tmax), we establish a pseudo-optimal formula for tmax calibrated against fractional Brownian motion of known dimensions. Finally, we enrich our analysis with random walk and power spectral density analysis, uncovering necessary empirical conditions for white-noise behavior and long-range dependence.",
  "abstract_shown": true,
  "affiliations": [
    "Department of IT, Huree College of ICT, Ulaanbaatar 16061, Mongolia",
    "Department of Computer Science, Huree College of ICT, Ulaanbaatar 16061, Mongolia",
    "Training Ship Operation Center, Gyeongsang National University, Tongyeong-si 53064, Republic of Korea"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Gang Gyoo Jin"
    },
    {
      "affs": [
        1
      ],
      "name": "Kwangcheol Shin"
    },
    {
      "affs": [
        2
      ],
      "name": "Jongkap Ahn",
      "orcid": "0000-0002-5733-5739"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/17hzb4krhn34h.bib",
  "cited_by": 0,
  "doi": "10.3390/fractalfract10100724",
  "fulltext_url": null,
  "id": "17hzb4krhn34h",
  "issns": [
    "2504-3110"
  ],
  "landing_url": "https://www.mdpi.com/2504-3110/10/10/724",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2002|Complex Systems and Time Series Analysis"
    ]
  ],
  "openalex": "W7221941280",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/17hzb4krhn34h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:32Z",
      "native_id": "10.3390/fractalfract10100724",
      "source": "crossref",
      "url": "https://www.mdpi.com/2504-3110/10/10/724"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2504-3110",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Fractal Dimension Analysis of Constants π and e Using Pseudo-Optimized Maximum Window Selection for the Higuchi Algorithm",
  "title_text": "Fractal Dimension Analysis of Constants π and e Using Pseudo-Optimized Maximum Window Selection for the Higuchi Algorithm",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:32Z",
  "url": "https://research.draconitic.com/paper/17hzb4krhn34h",
  "venue": "Fractal and Fractional",
  "versions": []
}