The protagonist of Oedipus Rex seems to be heading towards peace rather than horror. Elaborate, supporting your answer with examples.

I am afraid your original question didn't make sense, so I
had to edit it and try to guess at what you were originally meaning. I hope I got the
sense of the question right.

However, if this was your
question, I am afraid I have to disagree with it. Throughout the play there is a
brooding sense of the horror that the audience knows is going to befall Oedipus. This is
part of the dramatic irony of the text. We, as the audience, already know what Oedipus
sets himself to find out, and we can anticipate how this knowledge is going to impact
him. Thus it is that we watch his detective work through our fingers, dreading the
moment when all is revealed.

Unfortunately, when Oedipus is
"successful" in his investigations, his act of self-multilation, which is deeply
symbolic, clearly indicates the horror of this self-knowledge. Consider some of his last
words that clearly indicate the terror and sadness of his
position:

And
now what is left?

Images? Love? A greeting
even,

Sweet to the senses? Is there
anything?

Ah, no, friends: lead me
away.

Lead me away from
Thebes.

Lead the great
wreck

And hell of Oedipus, whom the gods
hate.

This play presents us
with the desperately tragic fate of one central character whom it is clear that the gods
have destined to suffer intensely and greatly. Therefore there is no sense of peace in
this play, and no arrival of any "happy ending." We leave this play disturbed by the
plight of the protagonist.