This is a reasonable candidate for a notion of a "Fractal" but these days it is generally accepted that there is no universal definition. For instance, this de

This is a reasonable candidate for a notion of a "Fractal" but these days it is generally accepted that there is no universal definition. For instance, this definition would not include objects such as the Devil's staircase [1] or more generally images of the unit interval under a continuous monotonically increasing function. Some more exposition about attempts to rigorously define the notion of a fractal can be find in the introduction to Kenneth Falconer's book [2] [1] https://en.wikipedia.org/wiki/Cantor_function https://en.wikipedia.org/wiki/Cantor_function [2] https://zbmath.org/1285.28011 https://zbmath.org/1285.28011 Edit: Fixed incorrect zbmath link.