As a writer, I like mystery when it comes to my characters. Because sometimes it is better to have a bit of mystery than to know all about the character. Although this would also depend on what kind of book you are writing to what kind of character you wish to portray. Mystery is good for some characters but not all and this is the same to kinds of books you are writing. So when I get to writing, I often look at how much if any mystery I want for my characters.
Take my short stories I have written, my main character, the killer, is a complete mystery, which I do on purpose because it gives a better sense of dread in my story. I like to think that when writing thrillers or horror books, mysterious characters can create more fear or scare for the reader. But this is not always the case. It really depends on how you want your book to turn out and the feeling behind your book.
I would love to hear how you create fear within the reader through your characters.
