Takagi Curve

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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.

Contributed by: Borut Levart (October 2008)
Open content licensed under CC BY-NC-SA


Snapshots


Details

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.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send