Why should anyone know such thing? It's enough to read about it: http://en.wikipedia.org/wiki/Gosper_island#Properties
This mathematical structure is simple enough and described so clearly, that implementation is with any reasonable graphics or UI library is really trivial. However, as you don't even certain about the language you want to use and did not tell us your platform (which is important in case of C++), I would have some doubts about your ability to do that.
Anyway, I wish you the best of luck. You are welcome to ask if you face with problems and have more specific questions.