Two kinds of mixing of periodical components according to the Spencer-Brown laws of form are considered. If the identical fragments of a periodic component remain unchanged, then the periodicity is of the penetrant (calling) form; if the identical fragments break up, then it is of the co-penetrant (crossing) form. The hidden periodicity of the penetrant form is studied using the symptom analysis; the co-penetrant form of periodicity is studied using the order asymmetry method. In the symptom analysis, the method of principal components and SSA are modified for finite geometries. The order asymmetry method is the cluster analysis where the distance between two gradations characterizes the deviation from the periodicity in a subsequence over these gradations.