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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. [ABSTRACT FROM AUTHOR]