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Information Dimension Of Galton Board

Author

Listed:
  • QIANLI ZHOU

    (Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China)

  • YONG DENG

    (Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China2School of Education, Shaanxi Normal University, Xi’an 710062, P. R. China3School of Knowledge Science, Japan Advanced Institute of Science and Technology, Nomi Ishikawa 923-1211, Japan4Department of Management, Technology, and Economics, ETH Zurich, Zurich 8093, Switzerland)

  • WITOLD PEDRYCZ

    (Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada)

Abstract

In this paper, we relax the definition of Rényi information dimension. The power law of the Entropy-Layer in the Galton board is discovered and we calculate its information fractal dimension. When the Galton board is extended to bias or three-dimensional space, we get the same fractal features. In addition, according to the connection between Pascal’s triangle and the Poisson distribution, we find constrained Poisson distribution groups with the same information dimension. This is the first time the information entropy is utilized to explore the fractal features of the Galton board and Pascal’s triangle.

Suggested Citation

  • Qianli Zhou & Yong Deng & Witold Pedrycz, 2022. "Information Dimension Of Galton Board," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-11, June.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:04:n:s0218348x22500797
    DOI: 10.1142/S0218348X22500797
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    Cited by:

    1. Zhou, Qianli & Deng, Yong, 2023. "Generating Sierpinski gasket from matrix calculus in Dempster–Shafer theory," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    2. Zhao, Tong & Li, Zhen & Deng, Yong, 2024. "Linearity in Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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