Starting with a triangle, the Takagi (or Blancmange) curve is the sum of a series of zigzag functions, each half the height of the previous one and with twice as many zigzags. In the limit the function is still continuous, but nowhere differentiable. Move the slider to increase the order of the curve and toggle the checkbox below to show the previous sum and the current step of the construction. The derivative is graphed on the right.
The curve is named after the Japanese mathematician Teiji Takagi who described it in 1903. Perhaps the curve is better known as the Blancmange function after its resemblance to a pudding of the same name.