Her obsession with finding a pattern reveals her imagination and creativity, which is stifled by her husband and by her being forced to spend so much time in the room.
She is depressed, not able to see her new baby, not permitted to have visitors, and shut in at all times. Since she is denied any opportunity for stimulation or creative outlet, she creates one. Her obsession with the wallpaper, and later the insanity it causes, show what kind of a mind she has. Her mind is one that needs to express itself creatively.
In "The Yellow Wallpaper," we learn about a woman who is being "treated" for a particular illness. We do not know what this is, although it is most likely a form of depression. However, the treatment she is being given is that of resting in a room with no mental stimulation.
This isolation causes the narrator to become obsessed with the wallpaper. What we learn is that the character has an intelligent, creative mind that needs to be stimulated. By depriving her of this, she slowly becomes more and more obsessed with the wallpaper, worsening her condition.
