Extra Stuff About Cyclic Permutations

Let us initially consider a phenomenology that goes through a state of a Fourier-related activity,  that is repeated over and over again -- yet, to where such a so-eluded-to general tendency of a cycle is to work to bear one or more slight changes, over the course of the iterations of each of such a so-eluded-to process or processes of cyclical states.  If the pattern of the cyclical changes, is never symmetrically completed -- in such a manner to where the overall pattern of such a general condition of a cycle is not equivalently iterative, then, such a cyclical pattern is said to diverge.  Yet, if the pattern of the cyclical changes, is to instead, be symmetrically completed in such a manner -- to where the overall pattern of such a general condition of a cycle is to be equivalently iterative, then, such a cyclical pattern is said to converge.  For instance -- let us consider an elliptical pattern, that is cyclical in permutation.  Let us say -- within a here considered tendency of time constraints -- that one physical phenomenology is to orbit around another physical phenomenology, in such a manner to where the tense of such an orbit, per each adjacent iteration of orbit, is to be slightly different is its precise Lagrangian-based contour, -- yet, let us say that in this given arbitrary case scenario, that after one thousand iterations of such an elliptical tendency of orbit, that the whole overall general pattern of a cyclical tendency is to be repeated in the exact same manner again, to where the second set of one thousand iterations of such an elliptical orbital-based tendency is to be exactly the same as the first set of one thousand iterations of such an elliptical orbital-based tendency.  In this just mentioned tense of a condition of cyclical permutation, the cycle is to here be symmetrical in its behavior, and thus, such a so-stated tense of a condition of cyclical permutation is to here be convergent, -- at least over the course of the first two thousand iterations of such a pattern of a cyclical-based permutation-related tense of elliptical orbit.  Furthermore, there are three general genre of Fourier-related cyclical permutations -- of which may sometimes be combined. There are Lagrangian-based cyclical-based permutations, and/or there are metrical-based cyclical permutations, and/or there are contour-based cyclical-based permutations.  I will later discuss what is meant by a Laplacian-related state of conditions, that would work to bear a tense of cyclical permutation.

I will continued with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.