Substitution systems and the three versions of distributional chaos

There are three types of distributional chaos, namely DC1, DC2 and DC3. In this paper we present two constant-length substitution systems, one is DC2 but not DC1, and the other is DC3 but not DC2. (In this paper, chaos means existence of an uncountable scrambled set of the corresponding type while the existing examples deal with single pairs of points only.)