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

Licensing

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You are free:

• to share – to copy, distribute and transmit the work
• to remix – to adapt the work

Under the following conditions:

• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
• share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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