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Takagi Curve

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.

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.
One difference between the Takagi curve and the slightly similar Koch snowflake is how their lengths change: the perimeter of the snowflake tends to infinity with increasing order, while the length of the Takagi curve stays fixed at the length of the initial tent ( in our case).

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