set pm3d depth lighting primary 0.65
set object rect from sc 0,0 to sc 1,1 behind fc "#003344" 
set palette defined (0 "salmon", 1 "khaki")
set samples 144
set isosamples 48
unset border
unset tics
unset colorbox
unset key
set xyplane 0
set view 70, 150, 1.8,
set term pngcairo size 360,360
set out "shell001.png"

set parametric
set urange [0:6*pi]
set vrange [0:2*pi]
a = 1.5
c = 4.1
set zrange [-2*c:0]
set xrange [-c:c]
set yrange [-c:c]

h(u) = exp(u/(6*pi))
x(u,v) = -a*(h(u)-1)*cos(u)*cos(v/2)**2
z(u,v) = 1 - exp(u/(3*pi)) - sin(v) + h(u)*sin(v)
y(u,v) = a*(h(u)-1)*sin(u)*cos(v/2)**2

splot x(u,v),y(u,v),z(u,v) w pm3d

!display "shell001.png"