| Abstract: | In this paper, we study some properties of Takagi functions and their level sets. We show that for Takagi functions $$T_{a,b}$$ with parameters a, b such that ab is a root of a Littlewood polynomial, there exist large level sets. As a consequence, we show that for some parameters a, b, the Assouad dimension of graphs of $$T_{a,b}$$ is strictly larger than their upper box dimension. In particular, we can find weak tangents of those graphs with large Hausdorff dimension, larger than the upper box dimension of the graphs. |
