The Weierstrass FunctionA line you can trace without lifting your pen, W(x) = Σ aⁿcos(bⁿπx) — yet it has no slope anywhere along it. Zoom in as far as you like: it never straightens into a tangent, it just keeps wiggling at a finer scale.Before 1872, mathematicians assumed a continuous curve had to be smooth almost everywhere. Weierstrass's sum of ever-finer, ever-flatter (but never fully damped) cosine ripples was a shock: a curve rough at every scale, with no scale where it ever looks straight. It's now seen as one of the first fractal curves, with a box-counting dimension between 1 and 2 that grows with a·b. This zoom probes that roughness directly — adding the higher frequencies your screen can newly resolve, forever.