# set terminal pngcairo  transparent enhanced font "arial,10" fontscale 1.0 size 500, 350 
# set output 'polar.9.png'
unset border
set style fill   solid 0.50 border
set dummy t,y
set grid polar 0.523599
set grid noxtics nomxtics noytics nomytics noztics nomztics \
 nox2tics nomx2tics noy2tics nomy2tics nocbtics nomcbtics
set grid layerdefault   linetype 0 linewidth 1.000,  linetype 0 linewidth 1.000
set key title "bounding radius 2.5"
set key outside right top vertical Right noreverse enhanced autotitles nobox
set key noinvert samplen 0.7 spacing 1 width 0 height 0 
set polar
set size ratio 1 1,1
set noxtics
set noytics
set rrange [ 0.100000 : 4.00000 ] noreverse nowriteback
set xrange [ -3.90000 : 3.90000 ] noreverse nowriteback
set yrange [ -3.90000 : 3.90000 ] noreverse nowriteback
butterfly(x)=exp(cos(x))-2*cos(4*x)+sin(x/12)**5
GPFUN_butterfly = "butterfly(x)=exp(cos(x))-2*cos(4*x)+sin(x/12)**5"
plot 3.+sin(t)*cos(5*t) with filledcurve above r=2.5 notitle,     3.+sin(t)*cos(5*t) with line