With patent quantity and GDP data, the author researched the quantitative relation between patent quantity, which is an output index of technological innovation, and Gross Domestic Product, which stands for the economic output of one country or region. Based on the analysis and calculation of 5 years data (from 1999 to 2003) of 31 provinces/cites of China, the author found out there is a strong correlation (the fitting correlation coefficient is 0.9434) between patent output and GDP of provinces/cites. This is a fractal, quantitative power function relation. In this article, the author discussed about the properties and meaning of this fractal, as well as the method of applying this quantitative relation for analyzing the technological innovation level and efficiency of region, and predicted its patent quantity and vice versa.