Abstract：The concepts, monopolized circle, monopolized line and monopolized sphere were put forward in this paper. The uniform index was put forward based on the study of the uniformity about finity point set. New concept measuring mapping was defined to fractal set, the fractal dimension of the fractal set can be transformed to the uniform index of the point set created by measuring mapping, it is shown that the complexity and uniformity are tight. The uniform index is a measure of point set pattern, which describes the spatial relationship in the point set, but the number. The uniform index can be any real number in interval, which is different from mathematical measure and fractal dimension. Two very interesting numbers, the uniform index of 1 digit infinite repeating decimal and random pattern are 0.1 and 1/x=0.318.