CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search Not to be confused with the Weierstrass elliptic function ( ) or the Weierstrass sigma, zeta, or eta functions . Plot of Weierstrass function over the interval [−2, 2]. Like fractals , the function exhibits self-similarity : every zoom (red circle) is similar to the global plot. In mathematics , the Weierstrass function is an example of a pathological real-valued function on the real line . The function has the property of being continuous everywhere but differentiable nowhere. It is named after its discoverer Karl Weierstrass . Historically, the Weierstrass function is important because it was the first published example (1872) to challenge the notion that every continuous function was differentiable except on a set of isolated points. [ 1 ] 1 Construction 2 Hölder continuit...