Devil's staircase

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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 $c(x)$.

Properties[edit]

Devil's staircase is continuous
Devil's staircase is not absolutely continuous

Videos[edit]

The Devil's Staircase | Infinite Series (19 May 2017)
Devil's Staircase (19 February 2017)
Intro Real Analysis, Lec 15, Uniform Continuity, Monotone Functions, Devil's Staircase, Derivatives (5 October 2016)
Cantor's staircase (25 November 2014)

References[edit]