{
  "annotation_id": "b01a2df9-76f4-4182-bc06-57f8e877847f",
  "date_created": "2026-03-02T18:01:10.263000Z",
  "date_modified": "2026-03-02T18:01:10.263000Z",
  "file_hash": "177be334286e4147703acba53f582045c138adb6903ba12c3b51ddd4d15f2027",
  "private": false,
  "record": {
    "abstract": "One-dimensional detrended fluctuation analysis (1D DFA) and multifractal\ndetrended fluctuation analysis (1D MF-DFA) are widely used in the scaling\nanalysis of fractal and multifractal time series because of being accurate and\neasy to implement. In this paper we generalize the one-dimensional DFA and\nMF-DFA to higher-dimensional versions. The generalization works well when\ntested with synthetic surfaces including fractional Brownian surfaces and\nmultifractal surfaces. The two-dimensional MF-DFA is also adopted to analyze\ntwo images from nature and experiment and nice scaling laws are unraveled.",
    "arxiv_id": "physics/0607194",
    "authors": [
      "Gao-Feng Gu",
      "Wei-Xing Zhou"
    ],
    "categories": [
      "physics.gen-ph",
      "physics.data-an"
    ],
    "doi": "10.1103/PhysRevE.74.061104",
    "journal_ref": "Physical Review E 74, 061104 (2006)",
    "title": "Detrended fluctuation analysis for fractals and multifractals in higher   dimensions",
    "url": "https://arxiv.org/abs/physics/0607194"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "98b9d99d-e17f-475f-952a-ea71cfbf386c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}