INFORMATION DIMENSION OF GALTON BOARD-Reference-Cited by-同舟云学术

INFORMATION DIMENSION OF GALTON BOARD

Published:2022-04-22 Issue:04 Volume:30 Page:
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

ZHOU QIANLI¹,DENG YONG¹²³⁴^ORCID,PEDRYCZ WITOLD⁵

Affiliation:

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

2. School of Education, Shaanxi Normal University, Xi’an 710062, P. R. China

3. School of Knowledge Science, Japan Advanced Institute of Science and Technology, Nomi Ishikawa 923-1211, Japan

4. Department of Management, Technology, and Economics, ETH Zurich, Zurich 8093, Switzerland

5. 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.

Funder

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X22500797

Reference44 articles.

1. Natural inheritance. By Francis Galton.

2. An Improved Mathematical Model of Galton Board With Velocity-Dependent Restitution

3. Randomness in a Galton board from the viewpoint of predictability: Sensitivity and statistical bias of output states

4. Optical Galton board

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