Abstract
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.
Highlights
Reference [6] summarizes the basic knowledge of fractal geometry, the relationship between fractal geometry and sustainable historical buildings in Vietnam, and the applicability of fractal geometry in drawing biological simulation architectural forms harmonious with nature, which is helpful in creating sustainable buildings for the future
Based on the above experimental preparation, it is assumed that the number of forms in indoor and outdoor building space is n, and the fractal data
The high fractal dimension value may be caused by the basic data, calculation methods, or application software built-in algorithms
Summary
Since Mandelbrot [1] put forward, the concept of fractal has quickly attracted the attention of various disciplines and become the main tool to describe complex and irregular geometric features. It is widely used in various fields such as architectural form, tunnel modeling, geological survey, and so on [2, 3]. Many types of research on an architectural form based on fractal theory have been carried out at home and abroad. Traditional two-dimensional fractal research masks the slowdown of plane expansion caused by height growth, and the architectural form presents increasingly strong three-dimensional characteristics [4, 5]. Fractals provide the quantitative and qualitative relationship between nature, the architectural environment, and computational mechanics
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