Murcio Roberto, Masucci A Paolo, Arcaute Elsa, Batty Michael
Centre for Advanced Spatial Analysis. University College London, First floor, 90 Tottenham Court Road, London, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062130. doi: 10.1103/PhysRevE.92.062130. Epub 2015 Dec 17.
We perform a multifractal analysis of the evolution of London's street network from 1786 to 2010. First, we show that a single fractal dimension, commonly associated with the morphological description of cities, does not suffice to capture the dynamics of the system. Instead, for a proper characterization of such a dynamics, the multifractal spectrum needs to be considered. Our analysis reveals that London evolves from an inhomogeneous fractal structure, which can be described in terms of a multifractal, to a homogeneous one, which converges to monofractality. We argue that London's multifractal to monofractal evolution might be a special outcome of the constraint imposed on its growth by a green belt. Through a series of simulations, we show that multifractal objects, constructed through diffusion limited aggregation, evolve toward monofractality if their growth is constrained by a nonpermeable boundary.
我们对1786年至2010年伦敦街道网络的演变进行了多重分形分析。首先，我们表明，通常与城市形态描述相关的单一分形维数不足以捕捉系统的动态变化。相反，为了恰当地描述这种动态变化，需要考虑多重分形谱。我们的分析表明，伦敦从一个可以用多重分形来描述的非均匀分形结构演变为一个均匀的结构，该结构收敛到单分形。我们认为，伦敦从多重分形到单分形的演变可能是绿化带对其增长施加限制的一个特殊结果。通过一系列模拟，我们表明，通过扩散限制聚集构建的多重分形对象，如果其增长受到不可渗透边界的限制，就会朝着单分形演变。
