基于分形维数测算的西安古城道路网研究

基于人类尺度营建的古城道路网经过历史演化具有分形结构.在汽车成为道路设计导向的背景下,立足于分形连接的古城道路网应回归人性化出行的视角,应用Hausdorff维数简化分析法,长度--半径维数分析法及分枝数目--半径维数分析法,对1735年,1893年,1949年及2014年四个时期西安古城道路网进行了分形维数的测算,揭示了道路网分形演化趋势和不同时期的分形特征,探讨了演化原因并确定了分形演化过程中的三个阶段(不断向更高层次演化阶段;演化到较高等级,但外部因素对道路网产生逆向扰动;处于较高层级,但交通方式变革使基于人类尺度的道路网在结构和功能上发生局部蜕变),指出目前西安古城道路网在结构和功能上的局部蜕化趋势不容忽视,并针对问题提出应推崇适宜步行和自行车出行的模式典范,对古城道路网保护乃至整个古城的可持续发展具有重要意义.

A fractal dimension study of road networks in the ancient city of Xi'an

The human-scale based road networks in ancient city finally have developed extraordinary fractal structure through lengthy historical evolution. Under the background that vehicle transportation rather than walking has been the oriented principle of road design, this paper holds out for the perspective that road networks with fractal connections in ancient city should focus more on humanized travel eagerly. The method of fractal geometry is chosen to reveal and study the characteristics and evolution of the road networks in the ancient city of Xi'an, which is taken as the typical research object in this paper. The fractal dimension values of the road networks in the ancient city of Xi'an in 1735 A.D., 1893 A.D., 1949 A.D. and 2014 A.D. are calculated via Hausdorff Fractal Dimension, Length-Radius Fractal Dimension and Dendrite-Radius Dimension methods. The detailed calculation is as follows: the Hausdorff Fractal Dimension value is 1.6412 in 1735 A.D., 1.6489 in 1893 A.D., 1.5913 in 1949 A.D. and 1.5744 in 2014 A.D.; the Length-Radius Dimension value is 1.7723 in 1735 A.D., 1.8147 in 1893 A.D., 1.8663 in 1949 A.D. and 1.9544 in 2014 A.D.; the Dendrite-Radius Dimension value is 1.6673 in 1735 A.D., 1.7024 in 1893 A.D., 1.9358 in 1949 A.D. and 1.928 in 2014 A.D. Based on the calculation above, the evolution trends of each three fractal dimensions have been traced out clearly, the road networks' fractal characteristics in different periods have been examined and the underlying mechanisms of fractal evolution have been discussed deeply and precisely. And then, three stages in fractal evolution processes of the road networks in the ancient city of Xi'an have been identified: (1) the road networks are evolving toward a higher level. In this stage, the values of the three fractal dimensions all increase continuously. Therefore, the road networks become increasingly sophisticated and advanced in structure and function; (2) the road networks have evolved into the high-level stage, but they are encountering perturbation. The fractal road networks are advanced and sophisticated in structure and function, but external factors that connected with wars and social instabilities let the road networks suffer from reversed perturbation. And the perturbation have imposed negative influences on the road networks with fractal structure absolutely; (3) the road networks remain in the high-level stage, but partial degeneration should not be neglected. In this stage, all the values of the three fractal dimensions stay in the high-value level, but two of the three fractal dimensions tend to decline. Although the road networks in the ancient city of Xi'an still possess the fractal structure, partial degeneration results from the change in the modes of transportation in the structure and function is obvious and pernicious. Next to the identification of the three stages above, this paper judges that the current system of the road networks in the ancient city of Xi'an makes the fractal structure more advanced and more sophisticated. But more attention is paid to the structural and functional degradation. Otherwise, malignant transmutation will be caused surely to disorder or even destroy the fractal road networks and the whole ancient city of Xi'an. Therefore, paradigmatic humanized city transportation modes of cycling and walking are highly recommended in this paper to preserve the road networks and to facilitate the sustainable development of the entire ancient city of Xi'an.