Uniform tag systems for paperfolding sequences

One folds lengthwise a strip of paper in p greater than or equal to 2 equal parts several times on itself (all folds being parallel). After unfolding, one obtains a sequence of ''valley'' and ''ridge'' folds. If one codes these folds over a two-letter alphabet, one obtains a p-paperfolding word associated with the sequence of p-folding instructions. A p-paperfolding sequence is an infinite p-paperfolding word. This paper is devoted to the effective construction of p-uniform tag systems which generate every p-paperfolding sequence associated with ultimately periodic sequence of p-(un)folding instructions.