  The celebrated Thue-Morse sequence, or the Prouhet-Thue-Morse sequence
(A010060 in the OEIS), has a number of interesting properties and is a rich
source to many (counter)examples. We introduce two different square-free
sequences on three letters with one of them is equivalent (up-to permutations
of letters) to Thue's original square-free sequence on three letters. Then we
use them to introduce an explicit method to construct infinitely many number of
recurrent points in ${\{0,1\}^{\mathbb{N}}}$ whose orbit closures under the
shift map is minimal, uncountable, and for any two distinct such points their
orbit closures are disjoint.
