In 1966, Kiesswetter found an interesting example of continuous everywhere but differentiable nowhere functions using base-4 expansion of real numbers. In this paper we show how Kiesswetter’s function can be extended to general cases. We also provide an equivalent form for such functions via a recurrence relation.
"Generalized Kiesswetter’s Functions." Real Anal. Exchange 40 (1) 141 - 156, 2013/2014.