De Rham curve

In mathematics, a de Rham curve is a certain type of fractal curve named in honor of Georges de Rham.

The Cantor function, Cesàro curve, Minkowski's question mark function, the Lévy C curve, the blancmange curve and the Koch curve are all special cases of the general de Rham curve.

Consider some metric space ${\displaystyle (M,d)}$ (generally ${\displaystyle \mathbb {R} }$² with the usual euclidean distance), and a pair of contracting maps on M:

By the Banach fixed point theorem, these have fixed points ${\displaystyle p_{0}}$ and ${\displaystyle p_{1}}$ respectively. Let x be a real number in the interval ${\displaystyle [0,1]}$, having binary expansion

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