Fractal dimension mathematically

[MCDOG1997]

How can i calculate the fractal dimension of a julia set with c=2?The question may be trivial, and I'm sorry if I'm waisting your time, but I understand so little from the theory on the internet that it's frustrating.

[Tglad]

It doesn't seem to be particularly easy, I would recommend a box counting method. The trick is that each pixel is coloured if any point within it is inside the set (not just the centre point), if you have a distance estimator then you colour the pixel of the centre is within half a pixel radius of the set (a good enough approximation I think).