Symbolism, Imagery, Allegory
It’s definitely not a coincidence that the woman in the wallpaper is trapped behind a pattern. Because so is the narrator.
Even before the woman in the wallpaper and the narrator merge into one (super creepy) being, they still have a lot in common. Ms. Wallpaper is trapped in an ugly yellow pattern that resembles a jail cell:
At night in any kind of light, in twilight, candlelight, lamplight, and worst of all by moonlight, it becomes bars! The outside pattern I mean, and the woman behind it is as plain as can be. (6.10)
But the narrator is trapped in a still uglier (and more cell-like) pattern: the pattern of being a woman in the 19th Century.
Women's lives were, according to Victorian norms, supposed to follow a strict trajectory. You achieved the bare minimum in education, got married, had babies, kept house. Your daughter did the exact same thing. Your granddaughter did the exact same thing. It was, to borrow a phrase, a vicious circle.
And within this larger vicious circle were the smaller repeating patterns of days. A middle-class Victorian woman like the narrator would have spent her time "managing the house," which meant telling servants what needed to be cleaned, what needed to be bought, and what needed to be cooked. It wasn't exactly hands-on...and it certainly wasn't variable.
So: two ladies trapped within a hideous, monotonous pattern. No wonder the narrator felt such an affinity with Ms. Wallpaper.