INFORMATION DIMENSION OF GALTON BOARD

Qianli Zhou (), Yong Deng and Witold Pedrycz ()
Additional contact information
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

FRACTALS (fractals), 2022, vol. 30, issue 04, 1-11

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.

Keywords: Information Dimension; Pascal’s Triangle; Fractal; Poisson Distribution; Uncertainty (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X22500797
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:30:y:2022:i:04:n:s0218348x22500797

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X22500797

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().