Math Speculation – Is There A ?Nano World For Functions Using Machine Learning Super Resolution?

If you zoom in on many functions they just look like a line. But nature does not look like that. There exist a nano world. Fine grained structures.

So I had the idea that you could let a machine learning network train on the few examples of fine grained resolution there is. Like ?fractals. And carry that information over to ordinary functions.

Could you have functions that hold more scale levels. That is. A smaller boundary. Where you still get meaningful information at the particular scale. It looks more interesting than a line at more scale levels. Whats the practical zoom level where you can still have some useful information of the function.

Could you use machine learning to first resemble a function A then turn it into a function B at higher zoom levels? 

Thats my math speculation for today.

Heres is an odd looking function. The two functions in one function function.