My name is James, from Canada. I have recently began doing fractal animations,
and I have been capturing fractals for the best part of two years now.
I have been posting incomplete and nearly complete works on Facebook, but
the copyright and privacy stuff seems a little sketchy to me. As well as Deviant Art.
I was thinking on starting my own website and buying a new domain. Any one else
have similar experiences in the matter, I'm sure u do. I am really looking forward to
sharing my art with the site and someday, the world!
Greetings, and Welcome to this particular Forum !!!

As Sockratease already stated, if you are worried about theft of your images, then do not put any full size works on the Internet. But then again, with several million fractal images already available online, the chance of theft will be almost nil.
If you are wanting to establish something so that you can sell your images, then may I suggest you read the following blog entry, along with the comments that follow:
http://orbittrap.ca/?p=1282 But if you just want to have a gallery to show off your works, then any online forum will suffice, and the free ones will save you the cost of a Domain Name and web hosting fees. Otherwise, there are ways to create your own for very little money these days.