The self-affine property of (U,r)(U,r)-Carlitz sequences of polynomials deciphered in terms of graph directed IFS

By defining the mmth graphical representation of a (U,r)(U,r)-Carlitz sequence of polynomials, we visualize the nonzero elements in a number table of coefficients of the first mm polynomials. When appropriately scaled, these graphical representations are compact sets contained in a fixed closed rectangle. We established the condition under which a subsequence of these scaled graphical representations converges to a compact set with respect to the Hausdorff metric. Furthermore, under the same condition, the limit set is shown to have self-affine property which can be deciphered in terms of graph directed self-affine iterated function system (GAIFS).