#
# Each vertex of the surface is also a hypertext anchor point that
# reports the complex values z and F(z)
#
save_encoding = GPVAL_ENCODING
set encoding utf8
set title offset 0,0
set title "Hyperbolic tangent of complex variable z = x + iy\n\n"

set label 1 at screen 0.08, 0.85 left
set label 1 "Surface shows abs(atanh(z))\nMouse-over reports Real and Imaginary components"

set xrange [ -pi/2 : pi/2 ]
set yrange [ -pi/2 : pi/2 ]
set urange [ -pi/2 : pi/2 ]
set vrange [ -pi/2 : pi/2 ]
set zrange [ 0 : pi/2 ]
set xtics 1 offset 0,-0.5
set ytics 1 offset 0,-0.5
set xtics add ("0\nx" 0)
set ytics add ("0\niy" 0)
set ztics format "%.1f"
set grid x y z vertical lw 1
set bmargin screen 0.03

set palette defined (0 "dark-blue", 0.5 "gold", 1 "dark-red")
set cbrange [0:pi/2]
unset colorbox
unset key
set sample 41
set isosample 41
set pm3d depthorder border lw 0.25 lighting spec2 0.4
set pm3d explicit
set view 45, 20, 1.0, 0.8
set xyplane at 0
set style textbox opaque noborder margin 2,6

F(x,y) = atanh(x + I*y)
surf(x,y) = abs(F(x,y))
text(x,y) = imag(F(x,y)) < 0 \
         ? sprintf(" %.2f - %.2f i ", real(F(x,y)), -imag(F(x,y))) \
         : sprintf(" %.2f + %.2f i ", real(F(x,y)), imag(F(x,y))) \

splot surf(x,y) with pm3d title "abs(atanh(z))", \
      '++' using 1:2:(surf(x,y)):(text(x,y)) with labels hypertext font ":Italic" \
           point lc rgb "0xff000000" pt 5 ps 2 notitle


Click here for minimal script to generate this plot