Isn't everything in real life fractal?

Question

I've learned that an object that its Hausdorff dimension strictly exceeds its topological dimension is a fractal - which implies that an object that has roughness everywhere is a fractal. However I think that all the objects in the real life has roughness everywhere in microscopic scale. Does that mean that everything we see is a fractal?

Answer 1

What microscopic scale? Go far enough and you have atoms and molecules. Is that what you want to talk about? Go still smaller and we have to use quantum mechanics. Is that what you want to talk about?

Fractals are mathematical objects. Some real-world objects, at some intermediate scales, are modeled well by fractals. I think that is the best we can say.