Weierstrass Nowhere-Differentiable Function
W(x) = Σ
aⁿ
cos(
bⁿ
πx), 0 < a < 1, ab > 1+3π/2
a (amplitude decay)
0.70
b (frequency mult)
7.0
Terms N
10
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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.