Devil's staircase

The Devil's staircase, also known as the Cantor function, is a function $c \colon [0,1] \rightarrow [0,1]$ can be expressed by the following rules:

1. Write $x$ in base-3.
2. If that representation of $x$ contains a $1$, replace every digit after the first $1$ with $0$'s.
3. Replace all $2$'s with $1$'s.
4. The resulting expansion defines $c(x)$.

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  Construction of $c$ in steps.

References

Cantor function