Perna Andrea, Kuntz Pascale, Douady Stéphane
Institut des Systèmes Complexes Paris Île-de France, 57-59 rue Lhomond, F-75005 Paris, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 2):066106. doi: 10.1103/PhysRevE.83.066106. Epub 2011 Jun 14.
We propose a method for quantitative characterization of spatial networklike patterns with loops, such as surface fracture patterns, leaf vein networks, and patterns of urban streets. Such patterns are not well characterized by purely topological estimators: also patterns that both look different and result from different morphogenetic processes can have similar topology. A local geometric cue--the angles formed by the different branches at junctions--can complement topological information and allow the quantification of the large scale spatial coherence of the pattern. For patterns that grow over time, such as fracture lines on the surface of ceramics, the rank assigned by our method to each individual segment of the pattern approximates the order of appearance of that segment. We apply the method to various networklike patterns and find a continuous but sharp dichotomy between two classes of spatial networks: hierarchical and homogeneous. The former class results from a sequential growth process and presents large scale organization, and the latter presents local, but not global, organization.
我们提出了一种用于定量表征具有回路的空间网络状图案的方法，例如表面裂缝图案、叶脉网络和城市街道图案。此类图案无法通过纯拓扑估计器得到很好的表征：外观不同且源自不同形态发生过程的图案也可能具有相似的拓扑结构。一种局部几何线索——不同分支在交叉点处形成的角度——可以补充拓扑信息，并允许对图案的大规模空间连贯性进行量化。对于随时间增长的图案，例如陶瓷表面的裂缝线，我们的方法为图案的每个单独段分配的秩近似于该段的出现顺序。我们将该方法应用于各种网络状图案，并发现两类空间网络之间存在连续但明显的二分法：分层网络和均匀网络。前一类源于顺序生长过程，呈现出大规模组织，而后一类呈现局部但非全局的组织。
