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