# set terminal pngcairo  background "#ffffff" enhanced font "times" fontscale 1.0 size 640, 480 
# set output 'complex_trig.1.png'
set format y2 "    "
unset key
set view map
set isosamples 100, 100
set size ratio 1 1,1
set style data lines
set xtics  norangelimit
set xtics   ("-\317\200/2" -1.57080, "-\317\200/4" -0.785398, "0" 0.00000, "\317\200/4" 0.785398, "\317\200/2" 1.57080)
set ytics  norangelimit
set ytics   ("-\317\200/2" -1.57080, "-\317\200/4" -0.785398, "0" 0.00000, "\317\200/4" 0.785398, "\317\200/2" 1.57080)
set y2tics border in scale 1,0.5 nomirror norotate  offset character 0, 0, 0 autojustify
set y2tics autofreq  norangelimit
set cbtics  norangelimit
set cbtics   ("0" -3.14159, "2\317\200" 3.14159)
set title "Color (Hue) indicates angle\nSaturation indicates amplitude" 
set xrange [ -1.57080 : 1.57080 ] noreverse nowriteback
set yrange [ -1.57080 : 1.57080 ] noreverse nowriteback
set cblabel "Phase Angle" 
set cblabel  offset character -2, 0, 0 font "" textcolor lt -1 rotate by -270
set cbrange [ -3.14159 : 3.14159 ] noreverse nowriteback
set palette positive nops_allcF maxcolors 0 gamma 1.5 color model HSV 
set palette defined ( 0 0 1 1, 1 1 1 1 )
Hue(x,y) = (pi + atan2(-y,-x)) / (2*pi)
phase(x,y) = hsv2rgb( Hue(x,y), sqrt(x**2+y**2), 1. )
GPFUN_Hue = "Hue(x,y) = (pi + atan2(-y,-x)) / (2*pi)"
GPFUN_phase = "phase(x,y) = hsv2rgb( Hue(x,y), sqrt(x**2+y**2), 1. )"
splot '++' using 1:2:(phase($1,$2)) with pm3d lc rgb variable