The Blancmange function, also called the Takagi fractal curve (Peitgen and Saupe 1988), is a pathological continuous function which is nowhere differentiable. 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 and to by steps of .
th iteration contains 
points, where 
, and can be obtained by setting 
, letting![b(m+2^(n-1))=2^n+1/2[b(m)+b(m+2^n)],](http://mathworld.wolfram.com/images/equations/BlancmangeFunction/NumberedEquation1.gif)
to 1 by steps of 
and 
to 
by steps of 
.