3D box-counting algorithm for calculating fractal dimension of cities

The traditional 2D box-counting fractal dimension algorithm has been extended to the 3D space and a 3Dbased box-counting fractal dimension algorithm was proposed.And the 2D and 3D algorithm were used respectively to study the fractal characters of city.Through comparing the results the fractal character of the spatial structure of cities along the third dimension was observed proving that the traditional fractal cities study based on two dimensional fractal dimension algorithm or simply adding 1 to the 2D fractal dimension to represent the 3D fractal dimension were not correct furthermore the correct method used in fractal city study was put forward.