Fractals are an interesting object from the computational point of view. They are often defined by iteration schemes, and hence are easy to compute. However, they also have fine structures rendering properties that are hard to compute. They are continuous objects, but their iteration definitions suggest that they be studied as discrete objects. In this talk, we introduce a Turing-machine based model of countinuous computation and discuss how to study the computational complexity of fractals in this model and how to apply the fractal constructions to other complexity problems of continous comptutation.