In the early twentieth century, a handful of French geographers and historians famously suggested that mainland France comprised two agrarian systems: enclosed field systems with scattered settlements in the central and western France and openfield systems with grouped settlements in eastern France. This division between grouped and scattered settlements can still be found on the outskirts of urban areas. The objective of this paper is to determine whether the shape of urban areas varies with the type of built patterns in their periphery. To this end, we identify and characterise the local and global deviations from scale invariance of built patterns in mainland France. For this, we propose a new method—Geographically Weighted Fractal Analysis—that can characterise built patterns at a fine spatial resolution without making any a priori distinction between urban patterns and suburban or rural patterns. By applying GWFA to the spatial distribution of buildings throughout mainland France we identify six geographically consistent types of built patterns that are distinctive in the way buildings are either concentrated or dispersed across scales. The relationship between the local built textures and the global shape of twenty metropolitan areas is then analysed statistically. It is found that the proportion of dispersed (or concentrated) outer suburban built patterns in metropolitan areas is closely related to the distance threshold that marks the morphological limit of their urban areas.

中文翻译：

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应用两种分形方法来表征整个法国大陆上建筑模式的尺度不变性的局部和全局偏差

在20世纪初期，少数法国地理学家和历史学家提出了一个著名的建议，即法国大陆包括两个农业系统：在法国中部和西部具有零星定居点的封闭田间系统和在法国东部具有成群定居点的开放田地系统。仍然可以在城市郊区找到分组居住和分散居住的区别。本文的目的是确定城市区域的形状是否随其周围建筑模式的类型而变化。为此，我们确定并描述了法国大陆建筑模式规模不变的局部和全局偏差。为了这，我们提出了一种新的方法-地理加权分形分析-可以在精细的空间分辨率下表征建筑模式，而无需在城市模式与郊区或乡村模式之间进行先验区分。通过将GWFA应用到整个法国大陆建筑物的空间分布中，我们确定了六种地理上一致的建筑模式类型，这些类型在建筑物集中或分散在各个尺度上的方式上是独特的。然后对二十个都会区的局部建筑纹理和整体形状之间的关系进行统计分析。结果发现，大都市区中分散的（或集中的）郊区郊区建筑模式的比例与标记城市区域形态极限的距离阈值密切相关。