"You know, Harry, in a way, you did see your father last night... You found him inside yourself." - Albus Dumbledore
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The Emperor is a stern father figure. He is the authority who determines the rules and regulations, the structure and order of his domain. The Emperor represents a charismatic leader who exercises forceful control, but he should also be careful to not become an overbearing tyrant.
Aside from Dumbledore himself, James Potter is perhaps the strongest role model to Harry through much of his childhood. Bold, popular, and talented, it's no wonder that Harry aspires to live up to his father through their many similarities. Though their personalities differ, there is no doubt that the memory of James serves as a guiding force to Harry in many of his actions.
The Emperor is often depicted with imagery of animal horns or antlers in his presence, as a reflection of his masculine instinct and vitality. I used the tree branches to suggest the same thing for James - as well as a subtle reference to his Animagus form.