In 1903, Takagi described a continuous, nowhere-differentiable function. Among its many properties, the Takagi function reflects the difference between the number of zeros and ones in binary expansions of integers. In this talk, we define deficit digit functions that consider k-nary expansions and weighted differences between digit counts. These functions give rise to generalizations of the Takagi function and enable us to explicitly describe weighted digit sums. We will also examine the graphs of these generalized Takagi functions and construct a new family of fractals. This work was done in collaboration with Michael Coons and Dylan Wood.
