Research On The Correlation Between Spatial Distribution Of Human Settlements And Fractal Landform Of Mahuyu Watershed In Northern Shaanxi

Based on urban planning theories and from aspect of fractal, supported by geographic information system(GIS), this paper chose Mahuyu watershed in Northern Shaanxi as study case and GIS、gridding dimension、correlation dimension as methods, aming to verify and summarize the fractal property and correlation between spatial distribution of human settlements and landform of study case, and to analyze reasons and existing problems behind the correlation to explore development paths for urban and rural settlements in Northern Shaanxi.As a branch of complex science, franctal seems like a new proposed theory, thought its study object has been existing in nature and the universe from the beginning and affecting the evolution of mankind. From shape perspective, the core feature of fractal object is that the whole shape and one part of it、one and another parts of it are all self-similar, like broccoli、pine tree and snowflake etc. From mathematics perspective, fractal object has non- integer dimension between 1and 2,2 and 3 due to that it’s either between line and plane or between plane and solid, and this non- integer dimension is called “fractal dimension”. Verified by some conclusions, the landform in Northern Shaanxi has branching self-similarity. This hypothesis therefore could be made that the human settlements in Northern Shaanxi also have similar fractal features and have some correlations with fractal landform in aspects of shape and mathematics.Based on above, this paper took two perspectives of shape and mathematics to complete this research from three main procedures as following. Firstly,the paer verified whether the landform and human settlements were fractal and came up with the conclusion that they all had obvious fractal features. Secondly, the paper summarized correlations between landform and settlements distribution form aspects of shape、location and structure, and came up with following conclusions:1) those two study objects had obvious leaf-like fractal feature from perspective of shape; 2) the scale of settlement was positively correlated with rank of river from perspective of location; 3) the whole feature of landform and settlements distribution was “subsequent branches connected by main branch” from perspective of structure. Thirdly, picking up one watershed as case and borrowing fractal model form others, this paper tried to put forward optimized plan based on the human-earth harmouious fractal relations. Compared with currant situation, the optimized plan proved probability of application of fractal. However, the application of fractal had its own limitation and shortage compared with traditional planning and hence the combinations of these two theories would have profound and lasting significance both for interdisciplinary research in urban planning and application exploration of fractal.