整体作为一个层次图捕捉空间的性质
Wholeness as a Hierarchical Graph to Capture the Nature of Space
摘要：
根据克里斯托弗·亚历山大的中心理论，一个整体由无数个递归定义的中心组成，这些中心是我们周围的事物或空间。整体性是一种全球结构或赋予生命的秩序，它从作为中心场的整体中浮现出来。整体性是任何复杂系统的基本组成部分，并在某种程度上存在于空间中。本文将整体性定义为一个层次图，其中各个中心表示为节点，它们之间的关系表示为有向链接。分层图的名字来自于由头/尾断裂揭示的固有缩放层次结构，这是一种用于重尾分布数据的分类方案和可视化工具。我们建议：（1）个体中心的整体性程度应该用PageRank（PR）分数来衡量，因为高生命度中心是指许多高生命度中心所指向的中心;（2）由头/尾断裂引起的层次水平或PR分数的ht指数可以表征整体的整体性程度：ht指数越高，整体的生命力或整体性就越强。应用于阿罕布拉建筑群和曼哈顿和瑞典的街道网络的三个案例研究表明，所定义的整体性相当好地捕捉了人类对地理空间生命程度的直觉。我们进一步建议，整体性的数学模型是一个重要的地理表示模型，因为它是拓扑导向，使我们能够看到底层的缩放结构。该模型可以指导地理设计，它应该被认为是整体扩展的转换，本质上就像种子或胚胎的展开过程，以创造美丽的建筑和自然环境或高度的整体性。
英文摘要：
According to Christopher Alexander's theory of centers, a whole comprises numerous, recursively defined centers for things or spaces surrounding us. Wholeness is a type of global structure or life-giving order emerging from the whole as a field of the centers. The wholeness is an essential part of any complex system and exists, to some degree or other, in spaces. This paper defines wholeness as a hierarchical graph, in which individual centers are represented as the nodes and their relationships as the directed links. The hierarchical graph gets its name from the inherent scaling hierarchy revealed by the head/tail breaks, which is a classification scheme and visualization tool for data with a heavy-tailed distribution. We suggest that (1) the degrees of wholeness for individual centers should be measured by PageRank (PR) scores based on the notion that high-degree-of-life centers are those to which many high-degree-of-life centers point, and (2) that the hierarchical levels, or the ht-index of the PR scores induced by the head/tail breaks can characterize the degree of wholeness for the whole: the higher the ht-index, the more life or wholeness in the whole. Three case studies applied to the Alhambra building complex and the street networks of Manhattan and Sweden illustrate that the defined wholeness captures fairly well human intuitions on the degree of life for the geographic spaces. We further suggest that the mathematical model of wholeness be an important model of geographic representation, because it is topological oriented that enables us to see the underlying scaling structure. The model can guide geodesign, which should be considered as the wholeness-extending transformations that are essentially like the unfolding processes of seeds or embryos, for creating beautiful built and natural environments or with a high degree of wholeness.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
