基于分形维数的游览路径复杂性分析--以留园为例

Complexity Analysis of Tour Route Based on Fractal Dimension:Taking Liuyuan as an Example

游览路径是联系园林空间与游者的媒介,对园林的游观体验起决定性作用。分形几何作为空间复杂性的度量方式,其对不规则形状的量化描述有优势,适合中国传统园林路径的量化研究。本研究基于对留园游览空间进行量化,根据其空间分形维度量化结果归纳其空间布局特征,并以空间布局特征为变量抽象、提取路径,计算其分形维数。通过相关性分析及多元回归分析,探讨空间布局对园林游览路径分形维数的影响,进一步讨论空间布局方式对游览体验的影响。结果表明:留园空间分形维度变化在空间尺度、曲折度变化和停靠空间处变化明显;空间尺度的变化可直接影响全局游览路径的分形维,而将停靠空间与空间的曲折度作为整体考量时,对全局游览路径的分形维数影响较大。

The tour path is the medium connecting the garden space and tourists,and plays a decisive role in the tour experience of the garden.As one of the measures of spatial complexity,the fractal geometry has advantages in the quantitative description of irregular shapes,which is suitable for the quantitative research of traditional Chinese garden paths.Based on the fractal theory,we quantify the tour space of lingering,and summarize its spatial layout characteristics according to its spatial fractal dimension distribution characteristics,then we extract the path with the spatial layout characteristics as variables,and calculate its fractal dimension.Through correlation analysis and multiple regression analysis,we discuss the influence mechanism of factors in spatial layout on the fractal dimension of garden tour path.The results show that the change of fractal dimension of Lingering Garden space is obvious in spatial scale,tortuosity and parking space;The change of spatial scale can directly affect the fractal dimension of the global tour path,and when the parking space and the tortuosity of space are considered as a whole,it has a great impact on the fractal dimension of the global tour path.