The **blancmange function **(also called the *Tagaki function *or curve) is a bumpy, pudding-shaped, nowhere differentiable function.

Originally called the Tagaki function, after its creator, it was renamed the blancmange function by Tall (1982).

## Notation for the Blancmange Function

The blancmange function is defined as the infinite series (Kearnes, n.d.):

Where h(x) = inf{|x−n| | n ∈ ℤ} is a sawtooth function of period 1.

In simpler terms, the blancmange function is like a fractal, made up of an infinite number of smaller “blancmanges.” It can be constructed by adding up sawtooth function iterations to infinity (Tall, 2013).

## References

Bailey, D. H.; Borwein, J. M.; Calkin, N. J.; Girgensohn, R.; Luke, D. R.; and Moll, V. H. Experimental Mathematics in Action. Wellesley, MA: A K Peters, pp. 111-113, 2007.

Dixon, R. Mathographics. New York: Dover, pp. 175-176 and 210, 1991.

Kearnes, K. The blancmange function. https://math.colorado.edu/~kearnes/Teaching/Courses/F18/Blancmange.pdfeitgen, H.-O. and Saupe, D. (Eds.). “Midpoint Displacement and Systematic Fractals: The Takagi Fractal Curve, Its Kin, and the Related Systems.” §A.1.2 in The Science of Fractal Images. New York: Springer-Verlag, pp. 246-248, 1988.

Tall, D. The Blancmange F. Continuous Everywhere but Differentiable Nowhere. The Mathematical Gazette. 66. 10.2307/3617301.

Tall, D. How Humans Learn to Think Mathematically: Exploring the Three Worlds of Mathematics. Cambridge University Press, 2013.

Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 16-17, 1991.

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