I'm going to ignore your fascinating and insightful vid commentary to say: your maths is wrong :D As I recall (and it's been a while)

Having a Hausdorf dimension...: bumpy at all magnifications.
Self similar: resembles itself shrunk/magnified

The coastline of australia is bumpy but not self similar.
An infinite straight line is self similar but not bumpy.
A fractal is self similar AND bumpy :)