{
  "annotation_id": "04265f3c-d27f-47a6-886b-ee65d6c60dc5",
  "date_created": "2026-03-02T18:00:35.387000Z",
  "date_modified": "2026-03-02T18:00:35.387000Z",
  "file_hash": "7bd624ce9887f4290744f372284d0f9ce77ed0d2a1bbf9409db0b8d982448681",
  "private": false,
  "record": {
    "abstract": "Fractal behavior and long-range dependence have been observed in an\nastonishing number of physical systems. Either phenomenon has been modeled by\nself-similar random functions, thereby implying a linear relationship between\nfractal dimension, a measure of roughness, and Hurst coefficient, a measure of\nlong-memory dependence. This letter introduces simple stochastic models which\nallow for any combination of fractal dimension and Hurst exponent. We\nsynthesize images from these models, with arbitrary fractal properties and\npower-law correlations, and propose a test for self-similarity.",
    "arxiv_id": "physics/0109031",
    "authors": [
      "Tilmann Gneiting",
      "Martin Schlather"
    ],
    "categories": [
      "physics.data-an",
      "math.PR",
      "nlin.CD"
    ],
    "doi": "10.1137/S0036144501394387",
    "journal_ref": "SIAM Review 46 (2004), 269-282",
    "title": "Stochastic models which separate fractal dimension and Hurst effect",
    "url": "https://arxiv.org/abs/physics/0109031"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "13183944-84aa-49c0-968f-2a331080be37",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}