Where does Sophocles accomplish catharsis in Oedipus Rex?

The catharsis is in the ending or resolution to the
drama.  It is here where the "cleansing" of both audience and protagonist is present. 
When Act IV is concluded, both Oedipus and the audience are both horrified at the news
of the shepherd.  It is at this moment, where much in way of filth has reached its
zenith.  Oedipus' pride, his boasting of free will, and his absolute confidence that he
can overcome the power of divined fate are illusions whose collision presens itself at
the end of Act IV, and whose shards open Act V.  Jocasta's suicide, at "being married to
her son and thus had given birth to his children," adds to the horrific filth that
presents itself to the audience.  The catharsis begins when Oedipus blinds himself. 
This allows him a chance to gain the same type of "sight" that Tieriesias, whom he
treated with scorn and disdain, possessed.  Yet, Sophocles is wise enough to know that
catharsis, or the act of purification has to happen on both political and personal
levels for this drama to meet the standard for the saga was only personal, but political
regarding a king and his obligation to his subjects.  It is for this reason that Oedipus
asks to face his subjects, blinded and humiliated.  As a broken man, one who seeks to
make right what he unknowingly made wrong, Oedipus asks for political forgiveness. 
However, where the true catharsis lies is not his how he wishes it for himself, but
rather for his children.  It is here where we begin to see purity and a sense of
reclamation evident, catharsis becoming formed before our very eyes.  Oedipus' own pride
has become secondary to the hopes for his children.  It is here where redemption and
restoration happens simultaneously for Oedipus and for the audience, who are reminded
that their own sins have to be seen in their larger context of an individual's life with
the closing words of the chorus.