Analysis of the Principle and Applications of Fractal
DOI:
https://doi.org/10.54097/5fxx1704Keywords:
Fractal geometry; Hausdorff dimension and measure; mechanical transmission; biomedical image.Abstract
As a matter of fact, fractal is one of the mystery in math applications which attracts a large number of scholars even in recent years. With this in mind, a brief introductions for definition of fractals and a presentation of a brief history of fractal theory will be presented in this study. To be specific, this study will provide explanations on basic principles of fractal geometry like self-similarity and scaling. At the same time, this study will also give the idea of fractal dimensions and examples of fractal shapes. In detail, the essay will include two specific fractal applications in mechanism and biomedicine. According to the analysis, challenges and limitations of fractal theory will be mentioned potential applications in various fields will be discussed. Eventually, this study will conclude summary of key points and importance of fractals in all fields. Overall, these results shed light on guiding further exploration of fractal investigation.
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References
Xie H, Xue X. China University of Mining and Technology. Mathematical Foundations and Methods in Fractal Applications. Science Press, 1997.
Kennech J F. Fractal geometry-mathematical foundations and applications. London: John Wiley & Sons, 1990.
Zhu H, Ji L. Fractal Theory and Its Application ™. Science Press, 2011.
Liu W. Study of the detection method of contact area of gear surface based on machine vision technique. Journal of Mechanical Transmission, 2013, 75(5): 18-26.
Miao X, Huang X. A complete contact model of a fractal rough surface. Wear, 2014, 309(1-2): 146-151.
Ciavarella M. Adhesive rough contacts near complete contact. International Journal of Mechanical Sciences, 2015, 104: 104-111
Liu L, Chen F, Yang W, et al. The model association and verification of the fractal dimension and the milling parameters. Mechanical Design and Manufacturing, 2015, 5: 122-126.
Zhao H, Wu R. Application Study of Fractal Theory in Mechanical Transmission. Acta of Chinese Engineering, 2016, 29(5): 9.
Ampilova N, Soloviev I P, Shupletsov Y V. On Application of Fractal Analysis Methods to Biomedical Preparation Images. Differential Equations & Control Processes, 2013.
Ampilova N, Gurevich E, Soloviev I. Application of Modified Fractal Signature & Regny Spectrum Methods to the Analysis of Biomedical Preparations Images. Proc. 6 Int. Conf. CEMA11 2013, 96-100.
Ampilova N., Soloviev I., Shupletzov Y. Multifractal spectrum as a classification sign for biomedical preparations images. Proc. 7 Int. Conf. CEMA12, 8-10 Nov. 2012, Athens, Greece, 2012, 98-101.
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