The proof doesn't assume that they are formed by not-too-pathological penstrokes.

<wrong>The idea is that you should measure the amount of black and white ink to change a symbol into another simbol, and if the total amount of ink is less than ε then they indistinguishable. (Where ε is some constant you must choose for the whole system.)</wrong>

I think that every horrible-totally-pathological ink splash has a nice indistinguishable version, but my real analysts is a bit rusty, and there are a few horrible things that I may have forgotten.

Edit: see comment below.