Turcotte D L, Pelletier J D, Newman W I
Department of Geological Sciences, Cornell University, Ithaca, NY 14853, USA.
J Theor Biol. 1998 Aug 21;193(4):577-92. doi: 10.1006/jtbi.1998.0723.
There are many examples of branching networks in biology. Examples include the structure of plants and trees as well as cardiovascular and bronchial systems. In many cases these networks are self-similar and exhibit fractal scaling. In this paper we introduce the Tokunaga taxonomy for the side branching of networks and his parameterization of self-similar side-branching. We introduce several examples of deterministic branching networks and show that constructions with the same fractal dimension can have different side-branching parameters. As an example of stochastic-branching in biology we consider the vein structure of a leaf. We show that the vein structure of the leaf and river networks have nearly identical side branching statistics. We introduce diffusion limited aggregation (DLA) clusters. These clusters also exhibit Tokunaga side-branching statistics. We consider several alternative explanations for why leaves, river networks, and DLA clusters have similar side-branching statistics. We also consider the allometric scaling relation between metabolic rate and the mass of species in terms of a cardiovascular system with Tokunaga statistics. We find reasonably good agreement between the observed scaling exponent, approximately 0.75, and our model for a range of values of the fractal dimension of the network and the blood flow resistance parameter.
生物学中有许多分支网络的例子。例如植物和树木的结构，以及心血管系统和支气管系统。在许多情况下，这些网络是自相似的，并呈现分形标度。在本文中，我们介绍了网络侧支的德永分类法及其自相似侧支的参数化。我们给出了几个确定性分支网络的例子，并表明具有相同分形维数的结构可以有不同的侧支参数。作为生物学中随机分支的一个例子，我们考虑了叶片的叶脉结构。我们表明，叶片的叶脉结构和河流网络具有几乎相同的侧支统计。我们介绍了扩散受限凝聚（DLA）簇。这些簇也呈现德永侧支统计。我们考虑了几种关于叶片、河流网络和DLA簇为何具有相似侧支统计的不同解释。我们还根据具有德永统计的心血管系统，考虑了代谢率与物种质量之间的异速生长标度关系。我们发现在观测到的标度指数（约为0.75）与我们针对一系列网络分形维数和血流阻力参数值的模型之间，有相当好的一致性。
