On the Number of Empty Cells in a Non-Homogeneous Allocation Scheme

Abdushukurov, F. A.; Chuprunov, A. N.

doi:10.1134/s1995080221020025

Cited by 1 publication

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“…We cover the study area with boxes of different scales, that is, we measure the two-dimensional and three-dimensional airspace with boxes or cuboids of different scales, or rectangles or cuboids of different scales and sizes, and count the number of scales covering the whole space, that is, the corresponding measure, which is called the number of nonempty boxes [14]. In one calculation, the scale of different scales should be kept constant; that is, the lengthwidth ratio should remain unchanged in the two-dimensional case and the length width height ratio should remain unchanged in the three-dimensional case.…”

Section: Principle Of 3d Box Dimension Algorithmmentioning

confidence: 99%

Fractal Design of Indoor and Outdoor Forms of Architectural Space Based on a Three-Dimensional Box Dimension Algorithm

Liang

et al. 2022

Mathematical Problems in Engineering

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The three-dimensional organic growth features of buildings have been given more and more attention according to the unique view representation regulations of the indoor construction industry, in order to optimize the usage and allocation efficiency of building space. To explore the configuration structure of building function space, the three-dimensional box dimension algorithm is used to measure the fractal dimension of the indoor and outdoor form of building space, and the two-dimensional and three-dimensional fractal characteristics of building space are compared and analyzed; the method of the second derivative is utilized for the automatic recognition of fractal scale-free areas, aiming at the imprecise problem of the artificial judgment of scale-free areas in earlier fractal research of interior and outdoor forms of architectural space. The experimental results show that the second derivative method can effectively and automatically identify the scale-free region. The coefficients of linear fitting are above 0.990, and the indoor and outdoor forms of architectural space have clear fractal characteristics. After applying the method, the three-dimensional fractal dimension grows, indicating that the interior and outdoor form usage of architectural space in this area is generally effective and compact.

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Section: Principle Of 3d Box Dimension Algorithmmentioning

confidence: 99%

Fractal Design of Indoor and Outdoor Forms of Architectural Space Based on a Three-Dimensional Box Dimension Algorithm

Liang

et al. 2022

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

On the Number of Empty Cells in a Non-Homogeneous Allocation Scheme

Cited by 1 publication

References 5 publications

Fractal Design of Indoor and Outdoor Forms of Architectural Space Based on a Three-Dimensional Box Dimension Algorithm

Fractal Design of Indoor and Outdoor Forms of Architectural Space Based on a Three-Dimensional Box Dimension Algorithm

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