dorsal/arxiv
View SchemaDetrended fluctuation analysis for fractals and multifractals in higher dimensions
| Authors | Gao-Feng Gu, Wei-Xing Zhou |
|---|---|
| Categories | |
| ArXiv ID | physics/0607194 |
| URL | https://arxiv.org/abs/physics/0607194 |
| DOI | 10.1103/PhysRevE.74.061104 |
| Journal | Physical Review E 74, 061104 (2006) |
Abstract
One-dimensional detrended fluctuation analysis (1D DFA) and multifractal detrended fluctuation analysis (1D MF-DFA) are widely used in the scaling analysis of fractal and multifractal time series because of being accurate and easy to implement. In this paper we generalize the one-dimensional DFA and MF-DFA to higher-dimensional versions. The generalization works well when tested with synthetic surfaces including fractional Brownian surfaces and multifractal surfaces. The two-dimensional MF-DFA is also adopted to analyze two images from nature and experiment and nice scaling laws are unraveled.
{
"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
}