If you have broad interests, should you describe a narrow research topic in statement of purpose anyways?
Why not do both?
The value of a narrow statement is to show that you are capable of focus and thinking deeply about a subject.  In fact, if one makes it too narrow, then it can exclude you from projects you would like because people think you won't be interested.

So you might formulate your statement as follows:


Start by expressing your broad interests and the accomplishments that you have made in the past.  For a Masters, it's more important to illustrate that you were able to build complex things than that those thing were novel.  Your breadth will be good here.
Shift to looking toward the future.  Express your desire to be doing something novel and intellectually significant. Then say, "For example, one thought that I have considered ... " and give a narrow statement focused on something that you think would be new and significant.  Just make it clear that it is a possible direction rather than something that you are committed to.