A 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 .

Peitgen and Saupe (1988) refer to this curve as the Takagi Fractal Curve.

**References**

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

Peitgen, 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.

Takagi, T. ``A Simple Example of the Continuous Function without Derivative.'' *Proc. Phys. Math. Japan* **1**, 176-177, 1903.

Tall, D. O. ``The Blancmange Function, Continuous Everywhere but Differentiable Nowhere.'' *Math. Gaz.* **66**, 11-22, 1982.

Tall, D. ``The Gradient of a Graph.'' *Math. Teaching* **111**, 48-52, 1985.

© 1996-9

1999-05-26