q(t, x, dx, n) = ( 1e-15 < abs(dx) && 0 < n ) ? \
                 q(t, x+dx, -(x + sin(x)- t)/(1+cos(x)), n-1): x/2

set style line 101 lt 0 lw 1 lc rgb "gray30"
set parametric
unset key
unset border
unset tics
set xr [-2:2]
set tr [-pi:pi]

set term pngc enh size 480,240
set out "mollweide.png"

set multiplot
plot 2*cos(t),sin(t) w filledc lc rgb "light-turquoise" 
plot 'world_110m.txt' using \
  (th=q(pi*sin($2/180*pi),2*asin($2/90),3e-14,10),($1/90)*cos(th)):\
  (sin(th))  w filledcurv lc rgb "dark-plum"
do for [i = 0:4] {
j = i*15.0/180*pi
th = q(pi*sin(j),2*asin(2*j/pi),3e-14,10 )
plot 0.5*i*cos(t), sin(t) ls 101, \
     cos(th)*t*2/pi, sin(th) ls 101, cos(th)*t*2/pi, -sin(th) ls 101
}
unset multiplot

!display mollweide.png