Calculation Of Fractal Dimension About Irregular Linear Objects

Fractal is a new theory and new discipline which is very popular and promising in the world.It was first proposed by the American mathematician BB Mandelbort in 1967 and now has been successfully applied to scientific research,engineering calculations and many other areas.Fractal dimension calculation of fractal objects is the basic content of the research.This paper focuses on the problem of fractal dimension calculation model of irregular line objects.it is proposed to be based on previous work to explore and obtain effective results about the irregular line object fractal calculation model by comparing and selectting of appropriate calculation models.The study selected typical irregular lines such as the Yangtze River,the Yellow River and the coastline at the small-scale scale in China as the research object.The data comes from the screen vectorization of the 1:8000000 map on the Yangtze River,the Yellow River and the coastline.On the basis.first,the fractal dimension theory is summarized,then two basic models—correction models and string variable models—are introduced for the research work.The limitations of the two models are pointed out through analysis,and the least squares of the results are calculated.Recalculating to contrast the differences in different calculation methods;Second,through the study of "uniformity theory",inspired by the exclusive ball theory,an external rectangle method based on ArcMap buffer analysis is proposed and tried.The power-law relationship of this method is proved,and then the fractal dimension of the circumscribed rectangular method and the uniformity under a certain measure are obtained through this power-law relationship;at the same time,the circumscribed rectangular method is introduced.Count the box dimension and calculate the box-counting dimension of the three objects.Finally,bring all the calculated fractal dimensions into the curve correction model to obtain the corresponding curve correction value.In this paper,the following results are obtained: A modified scheme for the existing modified and modified string model is proposed,aiming at reinterpretation by least squares;based on a new observation method: the circumscribed rectangle method to simulate the curve resolution changes And propose a related fractal dimension model for calculating two-dimensional curves;combined with the theory of fractal dimension in curve correction,the application of fractal calculation in map curve is given.The differences between different computational models in curve correction are compared;through the analysis and understanding of templates,try to use observer theory to interpret fractals and computational models.