Research On Establishing Method And Application Of Meta Fractal Dimension Model Based On DEM

Mandelbrot was the first person who discovered the self-similarity in complex phenomena by analyzing the length of Britain coastline, which led to the establishment of fractal geometry, so there was a close relationship between the fractal geometry and cartography. Fractal Dimension can be used to describe the degree of spatial complexity of the map objects as a quantitative index that reflects the ability of occupying the space. Fractal methods have had some applications in the field of cartography and GIS, such as the calculation of fractal dimension value of river and coastline, the analysis of urban structure, map generalization etc. However, all of these have been limited to the hypothesis that geography objects have relatively strict fractal character, namely self-similarity. But now some researches have shown that not all natural geographical phenomena possess simple linear self-similarity; rather, many depend on spatial or scale features. Further studies showed that when single geographical object or objects set was cross-affected by multiple factors, they would tend to show non-uniformity on spatial shape and distribution. In fact, different character inside of the object reflects the relation between the landform causes, the growth courses and the terrain complexity. Therefore a special attention must be paid to such a variable character when we try to apply the fractal theory to solve problems in the field of geography, and it is difficult to research this inside difference through the conversional fractal dimension methods. Then in 2002 a new method named Meta fractal dimension model is put forward by professor Long, and it is extensional of the fractal geometry methods.In this paper, based on the fractal analysis method, Meta fractal dimension method was applied into the digital terrain analysis through the DEM data. The concept model and the theory framework of the Meta Fractal Model were designed in the paper and the analysis software was also developed on the platform visual studio 6.0. It was proved that this method can describe the change rule of terrain complexity through the experiments. And the Meta fractal dimension index obtained by the calculation based on the Meta fractal model was applied into the landform research in northern Shaixi province. After many experiments, several conclusions were drawn in this paper. Firstly, the Meta fractal dimension index can quantificationally describe the terrain complexity, the higher of the value, more obvious of the terrain change. But the value will be less than 3 and when the terrain surface is flat, the value will be 2. It has a well corresponding relation between the growth courses of Loess landform and the distribution rule reflected by the Meta fractal dimension index through the multiple samples experiments. The research in the paper is the extension of the fractal analysis theory and its application, and also provide and new landform factor for digital terrain analysis.