What does the Uncharted Forest symbolize in Anthem by Ayn Rand?
Anthem, by Ayn Rand, is a highly allegorical (symbolic) novella; in a story like this, the names of people and places usually depict exactly what they are, and that is true of the Uncharted Forest.
From the very beginning of the story, the protagonist (Equality 7-2521) is intrigued by the Uncharted Forest, drawn to it like no one else seems to be and despite his own wishes. He says:
We do not wish to look upon the Uncharted Forest. We do not wish to think of it. But ever do our eyes return to that black patch upon the sky.
It is a place of legend and mystery, and the stories are all designed to keep anyone from trying to escape.
Men never enter the Uncharted Forest, for there is no power to explore it and no path to lead among its ancient trees which stand as guards of fearful secrets. It is whispered that once or twice in a hundred years, one among the men of the City escape alone and run to the Uncharted Forest, without call or reason. These men do not return.
When Equality 7-2521 is finally forced to run for his life, he runs through the Uncharted Forest, the place where he will find all the answers to the mysteries he has been wondering about for most of his life. As he makes his way through it, he finds the woman he loves (technically, she finds him) and they discover the house which begins to reveal the truth of the Unmentionable Times--and the pronoun "I."
The Uncharted Forest is also a symbol of nature in a very unnatural world. It is a place where Equality 7-2521 can live naturally and even begins to hunt with a bow. Nature in this novel is greater than trees and grass; the Uncharted Forest contains the elements of science which the Old Ones have no interest in exploring and, in fact, desperately want to suppress and keep hidden.
It is called the Uncharted Forest for a reason; it is a place which is unknown by and separated from the rest of the world by ignorance and fear. When Equality 7-2521 is finally free to explore, however, this is where he goes.