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.