Based on the angular backbone taken from the triangular Sierpinski gasket, several seLf-similar structures are disigned,
corresponding diffraction screens are made, and the Fraunhofer patterns as power spectra of them are given. Based upon a
viewpoint of generative production and by means of the ui-branched displacement operation, we have found the recurrence
formulae of spectral structure factor for these angular fractals. As a example, the recurrence formulae of power spectra for a
coherent point group is given, corresponding a series of curves as well as an isogram are plotted. The analysis of result shows
that the power spectra of this fractal point group has a rotation symmetry and a mirror symmetry, and appears a period doubling
phenomenon which follows the process of generative production.