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Creating a new monster character... I guess you could take one of four approaches to it:
- The "Fear Mythos" Approach: What themes and ideas do Bunnies generally symbolize, and how can you twist those?
- The "Silent Hill" Approach: What does the idea of bunnies and their motifs mean to you personally, and how can you twist that?
- The "Innocence Damned" Approach: How can you take something cute, like a bunny, and twist it into something horrific?
- The "Ruined Childhood" Approach: How could you twist something associated with innocence and youth (bunnies are baby rabbits, children are baby humans), and make it something horrible?
You should think all your options over first, however, before deciding on an idea for it. Then, once your theme is decided, think about how the monster behaves, acts, etc., what it does. Decide what your monster's basic motive is. For example, Slenderman (Slenderman Mythos) stalks and torments people psychologically, Pyramid Head (Silent Hill, specifically Silent Hill 2) punishes, Jason Voorhees (Friday the 13th) kills irresponsible teens. So, what's your monster do that makes it special? What's its Modus Operandi?
Once you have a theme and motive/personality for your monster, now you need to write a story with them that explores those themes and lets that monster's motive shine through. Going off my previous examples, the Slenderverse deals with mystery and obfuscation, Silent Hill 2 deals with guilt, and Friday the 13th deals with the consequences of being irresponsible with a child's life (especially if you're distracted by underage sex). So what's your story deal with? Tie it to your monster. The monster, remember, is the reflection of the story's message, theme, or big idea.
A lot of times, I find that horror deals with the fear of the unknown, or the fear of repercussions for one's actions, or simply the fear of something awful happening. Those seem to be very, very common themes. I could write a whole thesis paper and a half on themes in horror games, movies, novels, and other media. For example, everyone knows Mary Shelly wrote Frankenstein for a fun contest at a party with some author friends, but did you know Frankenstein is also essentially an allegory for the dangers of science going too far and the limits of human knowledge? H.P. Lovecraft dealt with very similar themes in much of his work, calling these limits "Things man was not meant to know" - literally, discoveries about the vast universe that for our own good, should stay hidden. Lovecraft also liked using the concept of human fragility, specifically human mental capacity, equating too much knowledge of dangerous stuff with madness in the most literal way possible. Edgar Allen Poe, meanwhile, also dealt with the fragility of the human psyche, but spoke more from emotional matters and intellectual ones, including the ever-present fear of death. There's a lot of overlap and it just makes horror such a fascinating genre. Don't be afraid to overlap or reinvent themes!