Spectra of fractal information on Cantor axis

Abstract

Four styles of fractal informations are constructed on the Cantor sets as time axis. Based upon a view point of generative production, we have found the recurrence formulae of spectral structure factor and of spectral shape factors of them, plotted a series of curves of the structure factor and four series of curves of the spectral functions. From the comparison and progression of these curves, it can be seen that the structure factor plays a ground role, and the shape factor plays a modulatory role, there are a competitive phenomena between generations in frequency domain. This investigation provides a basis for further understanding of the features of fractal informations by a new representation such as frequency domain.or the shape factor of specrta. Starting from the mother generation, and succeeding generations up to the Nth genration, the total spectra of N coexisting generations(NCG) is written as