Midpoint displacement

In mathematics, the blancmange curve is a fractal curve constructible by midpoint subdivision. It is also known as the Takagi curve, after Teiji Takagi who described it in 1901, or as the Takagi–Landsberg curve, a generalization of the curve named after Takagi and Georg Landsberg. The name blancmange comes from its resemblance to a pudding of the same name. It is a special case of the more general de Rham curve.

The blancmange function is defined on the unit interval by

where ${\displaystyle s(x)}$ is the triangle wave, defined by ${\displaystyle s(x)=\min _{n\in {\mathbf {Z}}}|x-n|}$, that is, ${\displaystyle s(x)}$ is the distance from x to the nearest integer.

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