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According to an interview with David Jaffe, Kratos' character was based off of Derek Vinyard from the film American History X.
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God of War III director Stig Asmussen has stated that David Jaffe, director of the original God of War, intended for Kratos to take on the Norse and Egyptian gods after killing Zeus and the Greek pantheon.
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Attachment Early screenshots of God of War shows Kratos' tattoo in the shape of the omega symbol on his head. Kratos' design had gone through several different changes in the games early development.
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In God of War, Cronos is shown with only four fingers. In later installment, he is shown with five.
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Kratos appears in actual Greek mythology as a Daimon or lesser god of strength. He is most notable for being the brother of Nike. Besides the coincidence of their name, this character bears no actual resemblance to the protagonist of the God of War series.