Image:Sine fixed point.svg

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Sine_fixed_point.svg‎ (SVG file, nominally 600 × 480 pixels, file size: 13 KB)

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[edit] Summary

Fixed point iteration of the sine function.

If using this as a starter for creating for iterative graphs, see Image:Cosine fixed point.svg for a superior, more abstracted method.

SVG replacement for Image:sine fixed point.png. Created in w:Gnuplot:

set term svg
set out "sine.svg"

set multiplot
set size ratio 0.5
unset key
set xrange [0:pi]
set yrange [0:1]
set xtics axis
set ytics axis
set border 3

unset parametric
set samples 100
plot x with lines lc 3
plot sin(x) with lines lc 3

set parametric
iter_y(y, n) = n >= 0 
iter_x(x, n) = n >= 0 

iter2_sin_x(x, n) = n>0 ? iter1_sin_x(sin(x), n-1) : x
iter1_sin_x(x, n) = n>0 ? iter2_sin_x(x, n-1) : x
iter_sin_x(x, n) = n>0 ? iter2_sin_x(x, n-1) : x
iter2_sin_y(y, n) = n>0 ? iter1_sin_y(y, n-1) : y
iter1_sin_y(y, n) = n>0 ? iter2_sin_y(sin(y), n-1) : y
iter_sin_y(y, n) = n>0 ? iter2_sin_y(sin(y), n-1) : 0
set samples 21
plot [0:20] iter_sin_x(2,t),iter_sin_y(2,t) with lines lc 1

unset multiplot

[edit] Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation license, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation license".