By using the frame representation method proposed by B. L. Hao et al. in 20001,2 and a method provided by P. Tino,3,4 we will devise the generalized graphical representation for the strings defined on an alphabet Σ = {0, 1, …, n - 1} with cardinal n but all these graphs are still shown in a unit square, and generate its corresponding struture tables automatically. In particular, the words defined on Σ are mapped into n-adic numbers so that the index set Ind(B) can be computed. Thus, the fractals of the forbidden words can be naturally constructed. It has already been known that for biological sequences, the circular codes can be applied to some special bacteria and their forbidden words are the 5-necklaces. In this paper, we notice that the fractals of the forbidden words are particularly useful to represent the circular codes for some biological sequences.
A hierarchy for circular codes
