Difference between revisions of "Takagi function"
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(Created page with "Define the function $s(x)=\min_{n \in \mathbb{Z}} |x-n|$. The Blancmange function is defined by $$\mathrm{blanc}(x)=\displaystyle\sum_{k=0}^{\infty} \dfrac{s(2^n x)}{2^n}.$$") |
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Define the function $s(x)=\min_{n \in \mathbb{Z}} |x-n|$. The Blancmange function is defined by | Define the function $s(x)=\min_{n \in \mathbb{Z}} |x-n|$. The Blancmange function is defined by | ||
$$\mathrm{blanc}(x)=\displaystyle\sum_{k=0}^{\infty} \dfrac{s(2^n x)}{2^n}.$$ | $$\mathrm{blanc}(x)=\displaystyle\sum_{k=0}^{\infty} \dfrac{s(2^n x)}{2^n}.$$ | ||
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| + | <div align="center"> | ||
| + | <gallery> | ||
| + | File:Blancmangefunction.png|Graph of $\mathrm{blanc}$ on $[0,1]$. | ||
| + | </gallery> | ||
| + | </div> | ||
Revision as of 19:18, 17 May 2015
Define the function $s(x)=\min_{n \in \mathbb{Z}} |x-n|$. The Blancmange function is defined by $$\mathrm{blanc}(x)=\displaystyle\sum_{k=0}^{\infty} \dfrac{s(2^n x)}{2^n}.$$
- Blancmangefunction.png
Graph of $\mathrm{blanc}$ on $[0,1]$.
