Other information

Gnuplot source (created by Jörn Nettingsmeier, CC-BY-SA 3.0 + GFDL)

set terminal pngcairo font "/usr/share/fonts/truetype/LiberationMono.ttf,8" size 512,512
set size square
set polar
set style line 11 lc rgb 'gray80' lt 1 lw 1
set style line 1 lc rgb 'red' lw 3 lt 1
set style line 2 lc rgb 'blue' lw 3 lt 1
set grid polar ls 11
unset border
unset raxis
unset xtics
unset ytics
unset key
set rrange[0:1.1]
set rtics ("" 1, "" 1/sqrt(2), "" .5, "" .5/sqrt(2), "" .25, "" .25/sqrt(2), "" .125)
set label 42 '0°' center at first 0, first 1.06
set label 43 '180°' center at first 0, first -1.06
set label 44 '90°' right at first -1.06, 0
set label 45 '270°' left at first 1.06, 0
set for [i=0:6] label (46+i) right at first 0.08, first (1/sqrt(2)**i) sprintf("%2d dB", i*-3.0) 
W(t)=1/sqrt(2)    
X(t)=sin(t)  # hack to turn 0° axis upwards
Y(t)=-cos(t) # dto.
#free-field normalised parametric microphone:
#gain functions for WXY:
GW(p)      = p * sqrt(2)
GX(T,p)    = (1.0-p)*cos(T)
GY(T,p)    = (1.0-p)*sin(T)
card(t,T,p)= GW(p)*W(t) + GX(T,p)*X(t) + GY(T,p)*Y(t)
#workaround to map negative r to positive but with blue color:
pcard(t,T,p) = card(t,T,p)>0 ? card(t,T,p) : 0
ncard(t,T,p) = card(t,T,p)>0 ? 0 : abs(card(t,T,p))

T=0 # point north!
p=1.0
frame=0
do for[a=0.0:47.0] {
  set output sprintf("polar-%03d.png",frame)
  frame=frame+1
  set label 1 left at first .62, first 1.08 sprintf("Theta: %3.1f°", (T*180.0/pi))
  set label 2 right at first 1.05, first 1.01 sprintf("Pattern: %1.6f", p)
  set label 3 right at first 1.05, first .91 sprintf("W: %1.6f", GW(p))
  set label 4 right at first 1.05, first .84 sprintf("X: %1.6f", GX(T,p))
  set label 5 right at first 1.05, first .77 sprintf("Y: %1.6f", GY(T,p))
  plot pcard(t,T,p) ls 1, ncard(t,T,p) ls 2
  p=p-1/72.0
}
do for[a=0.0:47.0] {
  set output sprintf("polar-%03d.png",frame)
  frame=frame+1
  set label 1 left at first .62, first 1.08 sprintf("Theta: %3.1f°", (T*180.0/pi))
  set label 2 right at first 1.05, first 1.01 sprintf("Pattern: %1.6f", p)
  set label 3 right at first 1.05, first .91 sprintf("W: %1.6f", GW(p))
  set label 4 right at first 1.05, first .84 sprintf("X: %1.6f", GX(T,p))
  set label 5 right at first 1.05, first .77 sprintf("Y: %1.6f", GY(T,p))
  plot pcard(t,T,p) ls 1, ncard(t,T,p) ls 2
  T=T-(pi/96.0)
}
do for[a=0.0:47.0] {
  set output sprintf("polar-%03d.png",frame) 
  frame=frame+1
  set label 1 left at first .62, first 1.08 sprintf("Theta: %3.1f°", (T*180.0/pi))
  set label 2 right at first 1.05, first 1.01 sprintf("Pattern: %1.6f", p)
  set label 3 right at first 1.05, first .91 sprintf("W: %1.6f", GW(p))
  set label 4 right at first 1.05, first .84 sprintf("X: %1.6f", GX(T,p))
  set label 5 right at first 1.05, first .77 sprintf("Y: %1.6f", GY(T,p))
  plot pcard(t,T,p) ls 1, ncard(t,T,p) ls 2
  p=p-1.0/144.0
}
do for[a=0.0:96.0] {
  set output sprintf("polar-%03d.png",frame) 
  frame=frame+1
  set label 1 left at first .62, first 1.08 sprintf("Theta: %3.1f°", (T*180.0/pi))
  set label 2 right at first 1.05, first 1.01 sprintf("Pattern: %1.6f", p)
  set label 3 right at first 1.05, first .91 sprintf("W: %1.6f", GW(p))
  set label 4 right at first 1.05, first .84 sprintf("X: %1.6f", GX(T,p))
  set label 5 right at first 1.05, first .77 sprintf("Y: %1.6f", GY(T,p))
  plot pcard(t,T,p) ls 1, ncard(t,T,p) ls 2
  p=p+1.0/96.0
  T=T-(1.5*pi/96.0)
}
set output