Where my creativity comes from and what influence my family has had are two different things
My creativity comes from my early childhood and asking one simple question "what next?" I had Willy Wonka and the Chocolate Factory read to me, and I said "that's good, what happened after that?" I couldn't find out (I didn't realise there was a sequel until later

) so I began a sequel I never finished. But I wrote 1 page with a picture and intended to finish it. I discovered that books often don't cover "What next?" so I began to daydream my own situations, but I didn't limit myself to books I'd read, I made up my own, just like the stories I read and tv shows I watched.
Sometimes I'd try to put it to paper, other times I'd act it out, other times I'd just think it up, entertain myself before forgetting it.
Now I seive everything I read and ask "could this be used for a story idea? Could this be used in an existing idea?" One example is I wanted to write a sci-fi/mystery set on a space-station orbiting Jupiter. But I couldn't think of a plot, only that I wanted to set it there. Possibly involving a son. Eventually I remembered about Europa and Io. Europa could be used to get water while Io could be harnessed to get thermal energy or something like that (still need to read a bit more). Eventually I remembered there's an asteroid belt in our solar system, so Jupiter station could be a pit-stop for miners working in the belt. I read
this article today from slashdot (which I visit daily). I saw a mention of Europa possibly having the life in it. I did a yahoo search while wikipedia was loading (it was running extremely slow) and saw an article on why Europa is the most likely place to have life outside of Earth. I saw Callisto (another Jupiter moon) has a liquid salt sea, but I saw that it's unlikely to have life. I read a wikipedia article and it mentioned something was crashed into Jupiter because there was fear as it's orbit decayed it would crash into Europa, so we'd never know if life on Europa was from Earth. And then I thought "hang on, what if my story idea has Jupiter station getting water from Callisto, and have Europa be preserved?" Later I was thinking in an imaginary conversation how I don't consider myself an Australian (completely unrelated to my story), I considered myself an Earthling. Then I thought well if we ever live outside such as on Mars I'd have to consider myself a citizen of Sol. I laughed as I realised that sounded like some crazy cult. I then thought back to my story idea and went "hey! What if there is such a terrorist organization/cult that wants to gain access to Europa, so it crashes Jupiter station into Europa, thus contaminating it? The cult's motivation would be to scour for life that may be a threat to Earth and neutralise it."
So for an idea that I've got in my head, it started out as "Something involving Jupiter station" to several weeks later an entire plot involving politics, extra-terrestial life and family relationships. And I'm working on a completely different short story before I even begin it (I also have many other ideas

).
The benefit to putting everything through my mental seive, is I'm finding a lot of information that justifies what I've decided for stories. For instance I wanted to have mars begun to be colonised, but have some of the colonists suffer from mutations. I decided why that was the case wasn't important, that isn't a focus of the story. I read today that Mars doesn't have a magentic-sphere (or something like that) in it's atmosphere, making Mars very prone to solar radiation. I fit it into my story, that's what causes the mutations. Is it important to the reader? No. Is it important to me? Yes, it makes the story more beleivable for me.
As for family influences, I could say my Dad wrote short stories for us kids that he read to us. But I believe creativity is a non-physical attribute and therefore isn't passed down from parent to child. I could say my Dad's a naturally great drawer, but I'm a pathetic one. I also am not naturally a writer, I work at my stories

I'm good at creating ideas, putting it to paper in an enjoyable format takes work for me though.
No my parents encouraged it by reading a Roald Dahl book to me when I was 8 (Willy Wonka and the Chocolate Factory). I loved it and having more of his books read to me. My parents got sick of it so I began reading books myself. My Dad recommended other authors to me, and I continued to expand from fantasy eventually to sci-fi. I enjoyed it a lot, it's only natural for me to want to create my own
