set or other fractals. While the Cantor function has derivative 0 almost everywhere, current research focusses on the question of the size of the set of points where the upper right derivative is distinct from the lower right derivative, causing the derivative to not exist. This analysis of differentiability is usually given in terms of fractal dimension, with the Hausdorff dimension the most popular choice. This line of research was started in the 1990s by Darst, who showed that the Hausdorff dimension of the set of non-differentiability of the Cantor function is the square of the dimension of the Cantor set, . Subsequently Falconer showed that this squaring relationship holds for all Ahlfor's regular, singular measures, i.e.Later, Troscheit obtain a more comprehensive picture of the set where the derivative does not exist for more general normalized Gibb's measures supported on self-conformal and self-similar sets. Hermann Minkowski's question mark function loosely resembles the Cantor function visually, appearing as a "smoothed out" form of the latter; it can be constructed by passing from a continued fraction expansion to a binary expansion, just as the Cantor function can be constructed by passing from a ternary expansion to a binary expansion. The question mark function has the interesting property of having vanishing derivatives at all rational numbers. See also Dyadic transformation Notes References Reprinted in: E. Zermelo (Ed.), Gesammelte Abhandlungen Mathematischen und Philosophischen Inhalts, Springer, New York, 1980. External links Cantor ternary function at Encyclopaedia of Mathematics Cantor Function by Douglas Rivers, the Wolfram Demonstrations Project. Fractals Measure theory Special functions Georg Cantor De Rham curves