In the final period of his life, Frankenstein pursues the creature with a newfound sense of purpose and determination. This is a dramatic departure from his previous attempts to flee from the creature and abandon his responsibility to it. The reason for this change lies in Frankenstein's realization that his creation is a reflection of himself and that he cannot escape his own guilt and responsibility.
Throughout the novel, Frankenstein repeatedly tries to disavow his creation and deny any connection to it. However, as he confronts the creature and witnesses the destruction it has wrought, he begins to recognize the ways in which he is responsible for its actions. He tells Walton, "I am the cause of all; I murdered her. William, Justine, and Henry — they all died by my hands" (Shelley, 187). Frankenstein acknowledges that he has been trying to escape his responsibility and that he cannot continue to do so.
Furthermore, Frankenstein realizes that the creature is a reflection of himself and that he cannot escape his own guilt and responsibility. He tells the creature, "I am thy creature: I ought to be thy Adam; but I am rather the fallen angel, whom thou drivest from joy for no misdeed" (Shelley, 142). This statement reflects Frankenstein's recognition that the creature is a product of his own ambition and that he cannot disown it without disowning himself.
In conclusion, Frankenstein pursues the creature in the final period of his life because he recognizes that he cannot escape his responsibility and that the creature is a reflection of himself. He realizes that he has been trying to disavow his creation and that he must confront it in order to face his own guilt and come to terms with his actions. The evidence from the text supports the idea that Frankenstein's pursuit of the creature is driven by his desire to take responsibility for his actions and make amends for the harm he has caused.