Difference between revisions of "Devil's staircase"
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(Created page with "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: # Write $x$ in base-3. # If...") |
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# Replace all $2$'s with $1$'s. | # Replace all $2$'s with $1$'s. | ||
# The resulting expansion defines $c(x)$. | # The resulting expansion defines $c(x)$. | ||
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| + | <div align="center"> | ||
| + | <gallery> | ||
| + | File:Cantor function.gif|Construction of $c$ in steps. | ||
| + | </gallery> | ||
| + | </div> | ||
=References= | =References= | ||
[http://en.wikipedia.org/wiki/Cantor_function Cantor function] | [http://en.wikipedia.org/wiki/Cantor_function Cantor function] | ||
Revision as of 10:59, 19 January 2015
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:
- Write $x$ in base-3.
- If that representation of $x$ contains a $1$, replace every digit after the first $1$ with $0$'s.
- Replace all $2$'s with $1$'s.
- The resulting expansion defines $c(x)$.
Construction of $c$ in steps.
