Weierstrass' example of an everywhere continuous but nowhere differentiable function is given by where λ ∊ (0, 1), b ⩾ 2, λb > 1. There is a well-known and widely accepted, but as yet unproven, formula for the Hausdorff dimension of the graph of w. Hunt [H] proved that this formula holds almost surely on the addition of a random phase shift. The graphs of Weierstrass-type functions appear as repellers for a certain class of dynamical system; in this paper we prove formulae analogous to those for random phase shifts of w(x) but in a dynamic context. Let T : S1 → S1 be a uniformly expanding map of the circle. Let λ : S1 → (0, 1), and define the function . The graph of w is a repelling invariant set for the skew-product transformation T(x, y) = (T(x), λ(x)−1(y − p(x))) on and is continuous but typically nowhere differentiable. With the addition of a random phase shift in p, and under suitable hypotheses including a partial hyperbolicity assumption on the skew-product, we prove an almost sure formula for the Hausdorff dimension of the graph of w using a generalization of techniques from [H] coupled with thermodynamic formalism.