The function whose values are

for any number between

and

Chalice (1991) shows that any real-valued function on [0, 1] which is Monotone Increasing and satisfies

- 1. ,
- 2. ,
- 3.

**References**

Chalice, D. R. ``A Characterization of the Cantor Function.'' *Amer. Math. Monthly* **98**, 255-258, 1991.

Wagon, S. ``The Cantor Function'' and ``Complex Cantor Sets.'' §4.2 and 5.1 in
*Mathematica in Action.* New York: W. H. Freeman, pp. 102-108 and 143-149, 1991.

© 1996-9

1999-05-26