  In this paper, we prove that an uncountable quantity of real numbers
generated by digital pattern sequences gives the transcendental number. This
result gives a generalization of Main theorem in Morton and Mourant [MortM],
which state that countable real numbers generated by digital pattern sequences
gives the transcendental number. Our method relies on the combinatorial
quantitative transcendence criterion established by Adamczewski-Bugeaud [AdB2]
and the properties of generalized $k$-regular sequences, which is introduced by
the author [Mi2].
