FRACTAL TOPOGRAPHY AND COMPLEXITY ASSEMBLY IN MULTIFRACTALS

Yi Jin, Junling Zheng, Jiabin Dong, Qiaoqiao Wang, Yonghe Liu, Baoyu Wang and Huibo Song
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Yi Jin: School of Resources and Environment, Henan Polytechnic University, Jiaozuo 454003, P. R. China†Collaborative Innovation Center of Coalbed Methane and Shale Gas for Central Plains Economic Region, Henan Province, Jiaozuo 454003, P. R. China
Junling Zheng: School of Resources and Environment, Henan Polytechnic University, Jiaozuo 454003, P. R. China‡Henan College of Industry and Information Technology, Jiaozuo 454003, P. R. China
Jiabin Dong: School of Resources and Environment, Henan Polytechnic University, Jiaozuo 454003, P. R. China
Qiaoqiao Wang: School of Resources and Environment, Henan Polytechnic University, Jiaozuo 454003, P. R. China
Yonghe Liu: School of Resources and Environment, Henan Polytechnic University, Jiaozuo 454003, P. R. China
Baoyu Wang: School of Resources and Environment, Henan Polytechnic University, Jiaozuo 454003, P. R. China
Huibo Song: School of Resources and Environment, Henan Polytechnic University, Jiaozuo 454003, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 03, 1-12

Abstract: Multifractals are the general form of scale invariances, where a fractal behavior is repeated by a similar object or pattern. Although the multifractal spectrum has been accepted as a measure of behavioral complexity, it cannot solely determine a fractal behavior, thus leaving the control mechanisms of multifractality unclarified. Here, we reexamine the multifractality, and discover two key features of scaling behaviors in the fractal behavior, i.e. multiplicity and repetition. Afterwards, we establish multifractal topography to unify the scale-invariance definition of arbitrary fractal behavior, clarify the physical meaning of singularity and its significance, construct a scale-invariance tree to delineate the control mechanisms in fractality, and then identify multifractals to be dual-complexity systems with the original and behavioral complexities controlling the scaling type and the scale-invariance property independently. This study gives insight into quantitative fractal theory and provides fundamental support for the mechanism exploration of nonlinear dynamics.

Keywords: Multifractality; Dual-Complexity System; Fractal Topography; Singularity; Hurst Exponent (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500529

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