The Blancmange function, also called the Takagi fractal curve (Peitgen and Saupe 1988), is a pathologicalcontinuous
function which is nowhere differentiable.
Its name derives from the resemblance of its first iteration to the shape of the
dessert commonly made with milk or cream and sugar thickened with gelatin.
The iterations towards the continuous function are batrachions resembling the Hofstadter-Conway
$10,000 sequence. The first six iterations are illustrated below. The th iteration contains points, where , and can be obtained by setting , letting
and looping over
to 1 by steps of
by steps of .
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