In the enotes explanation of Gilman's style, it is mentioned that Elaine R. Hedges wrote in the afterword to the 1973 edition of the story,
the [wall]paper symbolizes [the narrator's] situation as seen by the men who control her and hence her situation as seen by herself. How can she define herself?
As Gilman's narrator becomess obsessed with the lack of symmetry and pattern in what she perceives as the hideous yellow wallpaper, she perceives the design as ill-formed with a "sub-pattern in a different shade." This additional design is named by the narrator as a kind of
'debased Romanesque' with delirium tremens...in isolated columns of fatuity.
Thus, in her hallucinations, the narrator perceives the "provoking formless sort of figure" behind these columns that becomes a doppelganger, or paranormal double, for herself. Imagining the woman creeping around behind the pattern, the narrator transfers her obsession with the pattern to the "faint figure" that seems to shake this pattern in order to free herself. At this point, there is almost a gothic haunting or hallucination:
As soon as it was moonlight and that poor thing began to crawl and shake the pattern, I got up and ran to help her.
I pulled and she shook, I shook and she pulled, and before morning we had peeled off yards of that paper.
That the narrator believes the woman behind the pattern her double is evinced in her question,"I wonder if they all come out of that wallpaper as I did?" when, in freeing the woman/herself from the pattern she also imagines "strangled head and bulbous eyes" shrieking with derision.
In Gilman's story, then, the narrator defines herself in terms of an imprisoned woman surrounded by repressive figures who become the "bulbous eyes" she perceives in the symbolic wallpaper. It is this woman, her doppelganger, that the narrator feels she must free from the domination of others.