The function has detail at every level, so zooming in on a piece of the curve does not show it getting progressively closer and closer to a straight line. Rather between any two points no matter how close, the function will not be monotone. The Hausdorff dimension D of the graph of the classical Weierstrass function is bounded above by 2 + logba, (where a and b are the constants in the construction above) and is generally believed to be exactly that value, but this has not been proven rigorously.[5][6] Notice that 1 < D < 2 if ab > 1.