The escape time algorithm cannot render the convergence region of mapping, so there are some black regions in escape time fractal. In this paper, a novel method is presented to construct fractal image, which is named the distance ratio iteration method. This method performs iteration on two points and render fractal image by using their distance ratio convergence times. Taking complex mapping z←z^α+c as example, the generalized Mandelbrot and Julia sets are constructed based on distance ratio and their visual properties are analyzed. The result fractal image has complex and self-similarity structure in inner convergence region. It is proved that the boundary of distance ratio fractal is the same as M-J set when α>0, and some visual structure of it with various exponent α are discussed. When α<0, the generalized Mandelbrot and Julia set based on distance ratio have some complex structures which M-J set does not have.