The Weierstrass nowhere differentiable function, and functions constru
cted from similar infinite series, have been studied often as examples
of functions whose graph is a fractal. Though there is a simple formu
la for the Hausdorff dimension of the graph which is widely accepted,
it has not been rigorously proved to hold. We prove that if arbitrary
phases are included in each term of the summation for the Weierstrass
function, the Hausdorff dimension of the graph of the function has the
conjectured value for almost every sequence of phases. The argument e
xtends to a much-wider class of Weierstrass-like functions.