A Comparative Study of Fractal Models Applied to Artificial and Natural Data
This paper presents an original and comprehensive comparative analysis of eight fractal analysis methods, including Box Counting, Compass, Detrended Fluctuation Analysis, Dynamical Fractal Approach, Hurst, Mass, Modified Mass, and Persistence. These methods are applied to artificially generated frac...
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MDPI AG
2025-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/2/87 |
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| author | Gil Silva Fernando Pellon de Miranda Mateus Michelon Ana Ovídio Felipe Venturelli João Parêdes João Ferreira Letícia Moraes Flávio Barbosa Alexandre Cury |
| author_facet | Gil Silva Fernando Pellon de Miranda Mateus Michelon Ana Ovídio Felipe Venturelli João Parêdes João Ferreira Letícia Moraes Flávio Barbosa Alexandre Cury |
| author_sort | Gil Silva |
| collection | DOAJ |
| description | This paper presents an original and comprehensive comparative analysis of eight fractal analysis methods, including Box Counting, Compass, Detrended Fluctuation Analysis, Dynamical Fractal Approach, Hurst, Mass, Modified Mass, and Persistence. These methods are applied to artificially generated fractal data, such as Weierstrass–Mandelbrot functions and fractal Brownian motion, as well as natural datasets related to environmental and geophysical domains. The objectives of this research are to evaluate the methods’ capabilities in capturing fractal properties, their computational efficiency, and their sensitivity to data fluctuations. Main findings indicate that the Dynamical Fractal Approach consistently demonstrated the highest accuracy across different datasets, particularly for artificial data. Conversely, methods like Mass and Modified Mass showed limitations in complex fractal structures. For natural datasets, including meteorological and geological data, the fractal dimensions varied significantly across methods, reflecting their differing sensitivities to structural complexities. Computational efficiency analysis revealed that methods with linear or logarithmic complexity, such as Persistence and Compass, are most suited for larger datasets, while methods like DFA and Dynamic Fractal Approaches required higher computational resources. This study provides an original comparative study for researchers to select appropriate fractal analysis techniques based on dataset characteristics and computational limitations. |
| format | Article |
| id | doaj-art-6afcb52fbae1429faa36f072eccacdfd |
| institution | DOAJ |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-6afcb52fbae1429faa36f072eccacdfd2025-08-20T03:12:08ZengMDPI AGFractal and Fractional2504-31102025-01-01928710.3390/fractalfract9020087A Comparative Study of Fractal Models Applied to Artificial and Natural DataGil Silva0Fernando Pellon de Miranda1Mateus Michelon2Ana Ovídio3Felipe Venturelli4João Parêdes5João Ferreira6Letícia Moraes7Flávio Barbosa8Alexandre Cury9PETROBRAS—Petróleo Brasileiro S/A, Rio de Janeiro 20231-030, RJ, BrazilPETROBRAS—Petróleo Brasileiro S/A, Rio de Janeiro 20231-030, RJ, BrazilPETROBRAS—Petróleo Brasileiro S/A, Rio de Janeiro 20231-030, RJ, BrazilFaculty of Engineering, Federal University of Juiz de Fora, Juiz de Fora 36036-090, MG, BrazilFaculty of Engineering, Federal University of Juiz de Fora, Juiz de Fora 36036-090, MG, BrazilFaculty of Engineering, Federal University of Juiz de Fora, Juiz de Fora 36036-090, MG, BrazilFaculty of Engineering, Federal University of Juiz de Fora, Juiz de Fora 36036-090, MG, BrazilFaculty of Engineering, Federal University of Juiz de Fora, Juiz de Fora 36036-090, MG, BrazilGraduate Program in Civil Engineering, Federal University of Juiz de Fora, Juiz de Fora 36036-090, MG, BrazilGraduate Program in Civil Engineering, Federal University of Juiz de Fora, Juiz de Fora 36036-090, MG, BrazilThis paper presents an original and comprehensive comparative analysis of eight fractal analysis methods, including Box Counting, Compass, Detrended Fluctuation Analysis, Dynamical Fractal Approach, Hurst, Mass, Modified Mass, and Persistence. These methods are applied to artificially generated fractal data, such as Weierstrass–Mandelbrot functions and fractal Brownian motion, as well as natural datasets related to environmental and geophysical domains. The objectives of this research are to evaluate the methods’ capabilities in capturing fractal properties, their computational efficiency, and their sensitivity to data fluctuations. Main findings indicate that the Dynamical Fractal Approach consistently demonstrated the highest accuracy across different datasets, particularly for artificial data. Conversely, methods like Mass and Modified Mass showed limitations in complex fractal structures. For natural datasets, including meteorological and geological data, the fractal dimensions varied significantly across methods, reflecting their differing sensitivities to structural complexities. Computational efficiency analysis revealed that methods with linear or logarithmic complexity, such as Persistence and Compass, are most suited for larger datasets, while methods like DFA and Dynamic Fractal Approaches required higher computational resources. This study provides an original comparative study for researchers to select appropriate fractal analysis techniques based on dataset characteristics and computational limitations.https://www.mdpi.com/2504-3110/9/2/87fractal analysisfractal dimensioncomparative studyartificial datanatural data |
| spellingShingle | Gil Silva Fernando Pellon de Miranda Mateus Michelon Ana Ovídio Felipe Venturelli João Parêdes João Ferreira Letícia Moraes Flávio Barbosa Alexandre Cury A Comparative Study of Fractal Models Applied to Artificial and Natural Data Fractal and Fractional fractal analysis fractal dimension comparative study artificial data natural data |
| title | A Comparative Study of Fractal Models Applied to Artificial and Natural Data |
| title_full | A Comparative Study of Fractal Models Applied to Artificial and Natural Data |
| title_fullStr | A Comparative Study of Fractal Models Applied to Artificial and Natural Data |
| title_full_unstemmed | A Comparative Study of Fractal Models Applied to Artificial and Natural Data |
| title_short | A Comparative Study of Fractal Models Applied to Artificial and Natural Data |
| title_sort | comparative study of fractal models applied to artificial and natural data |
| topic | fractal analysis fractal dimension comparative study artificial data natural data |
| url | https://www.mdpi.com/2504-3110/9/2/87 |
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