set pm3d depth lighting 
set object rect from sc 0,0 to sc 1,1 behind fc "#114400"
set palette defined (0 "#ff9933", 1 "#ff9933")
set samples 128
set isosamples 128
unset border
unset tics
unset colorbox
unset key
set xyplane 0
set view 60,30, 1.2, 1.4
set term pngcairo size 360,360
set out "stool.png

f(x,y) = x**6+3*y**2*x**4+(3*y**4-4*y**2)*x**2+y**6

c = 1
zc = f(1,1)
set xrange[-c:c]
set yrange[-c:c]
set zrange[-zc-0.5:1.5]

splot -f(x,y) w pm3d 
!display "stool.png"