Thanks!! I was also under the impression Fractals required self similarity and not just infinite detail but glad to have that misconception corrected!
I think it probably stems from the fact that all the fractals, I have seen, for which the dimension can be analytically calculated do show obvious patterns of similarity at different scales.
Searching I stumbled over this paper[1], which I found interesting, on characterizing the fractal-ness of geological structures.
They point out that the usual measure of fractal dimension, or capacity dimension[2], doesn't consider the physical size of the features and can thus be inaccurate. Instead they suggest using the information dimension[3], which is bounded by the capacity dimension.
I think it probably stems from the fact that all the fractals, I have seen, for which the dimension can be analytically calculated do show obvious patterns of similarity at different scales.