File:Fracit05t150.jpg
Revision as of 21:24, 4 August 2013 by T (talk | contribs) (Iterate of linear fraction; $\displaystyle f(z)=\frac{x}{c+z}$ at $c\!=\!0.5$. In general the $n$th iterate of $f$ can be expressed as follows: $\displaystyle f^n(z)=\frac{z}{c^n+\frac{1-c^n}{1-c} z}$ $y=f^n(x)$ is plotted versus $x$ for vario...)
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$\displaystyle f(z)=\frac{x}{c+z}$ at $c\!=\!0.5$.
In general the $n$th iterate of $f$ can be expressed as follows:
$\displaystyle f^n(z)=\frac{z}{c^n+\frac{1-c^n}{1-c} z}$
$y=f^n(x)$ is plotted versus $x$ for various values of $n$.
Generator of curves
// File ado.cin should be loaded to the working directory in order to compile the C++ code below.
//
..
//
Latex generator of labels
%File Fracit20t.pdf should be generated with the code above in order to compile the Latex document below.
%
\documentclass[12pt]{article}
%
References
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 21:24, 4 August 2013 | | 1,466 × 1,466 (441 KB) | T (talk | contribs) | Iterate of linear fraction; $\displaystyle f(z)=\frac{x}{c+z}$ at $c\!=\!0.5$. In general the $n$th iterate of $f$ can be expressed as follows: $\displaystyle f^n(z)=\frac{z}{c^n+\frac{1-c^n}{1-c} z}$ $y=f^n(x)$ is plotted versus $x$ for vario... |
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