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

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