A class of practically nowhere differentiable functions on the complex plane

This note could find classroom use in an introductory course on complex analysis. Using some of the most significant theorems from complex analysis, the main result provides a simple method for transforming many elementary functions (defined on the complex plane) into everywhere continuous functions that are differentiable only on a nowhere dense set. Accordingly, such continuous functions are termed 'practically nowhere differentiable'. The twofold pedagogical value of this method is that (1) students can readily generate examples of everywhere continuous, practically nowhere differentiable functions that do not require any direct appeal to infinite series, and (2) the often dynamical difference between the behaviour of functions of a complex variable and functions of a real variable is showcased.