In this paper, three modes of self-similar time informations on Cantor's fractal axis are constructed. Based upon a theoretical view point of generative production, we have found the recurrence formulae of spectral structure factor and shape factor of them, and plotted four series of spectral curves. By the comparison and progression of spectral curves, it can be seen that the structure factors play the ground role and the shape factors play the modulatory role, and there are competitive phenomena between generations. This investigation provides a basis for further understandng of the characteristics of self-similar informations by a new representation such as frequency domain.