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

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.

Optimization of Dynamic Graphic Packaging Design Scheme Based on Graph Neural Network

“…In the process of constantly improving the function, structure, and environmental protection of packaging design, the visual communication of packaging is also constantly pursuing the humanized development. Product packaging is the composition of product function and value, and dynamic graphic design is one of the important elements of product packaging [13,14].…”

Research on Gridding of Urban Spatial Form Based on Fractal Theory

“…Traditional 2D fractal research aims to reveal the plane shape of a city, but it struggles to reflect the changes in a city's 3D space. There are even a small number of pioneering scholars trying to expand the research scale of urban space into 3D [30][31][32]. However, there is a lack of research combining 2D and 3D fractal analysis, despite the clear benefits.…”

“…First, the visualization capability of fractal results is low. Planners and decision-makers are often unable to intuitively obtain the specific form of urban space from the digital fractal results [30][31][32][33]. Secondly, the scale of urban fractal research is relatively macro, thus the spatial morphological differences in different areas of the city cannot be displayed [34][35][36].…”

Urban spatial form analysis based on the architectural layout -- Taking Zhengzhou City as an example

“…A city is a three-dimensional(3D) entity, and a traditional 2D fractal cannot often accurately express the impact of building height on urban space [30]. Thus, recently, some researchers have tried using 3D fractals to study urban spatial morphology, mainly using 3D box-counting methods to analyse the evolution of urban 3D space and the spatial morphology and change trends of buildings with different functions [30][31][32]. Relevant research has proven that urban spatial forms exhibit obvious 3D fractal characteristics.…”

“…Based on the above, the morphological characteristics and evolution trend of the architectural space in the outer ring of Zhengzhou City are analysed from 2D and 3D perspectives. This research has certain significance to the quantification of urban architectural form and the visualization research of fractal theory [34][35][36][37][38][39]. Furthermore, to our knowledge, gradient analysis and fractal theory have been combined for the first time, strengthening the direction of urban development and making the information acquisition of urban planning and decision making more intuitive.…”