Weierstrass Nowhere-Differentiable Function

W(x) = Σ aⁿ cos(bⁿπx),   0 < a < 1, ab > 1+3π/2
0.70
7.0
10
0
Weierstrass 1872: shocked mathematicians who believed continuous = differentiable almost everywhere.
Hausdorff dimension D = 2 + log(a)/log(b) for ab > 1+3π/2. Self-similar structure at all scales.