diff --git a/barbot.plt b/barbot.plt
index 370589a..fdac2e1 100644
--- a/barbot.plt
+++ b/barbot.plt
@@ -1,45 +1,41 @@
 set size ratio 1.3
 set grid
-set xrange [0:2.5]
-set yrange [0:5]
-set samples 1000
+set xrange [1/2.5:2.5]
+set yrange [0.2:5]
+set samples 2000
 set parametric
 
-# set terminal pngcairo size 1000, 1200
-# set output "barbot.png"
+set log x
+set log y
+
+set terminal pngcairo size 1000, 1200
+set output "barbot-symmetric.png"
 
 # solves the equation rho(s)q^2 - (s+1)q + 1 = 0
 # (s^2 + cs + 1)q^2 - (s+1)q + 1 = q^2 s^2 + (cq - 1)qs + (q^2 - q + 1)
 c = 2*cos(4*pi/5)
 rho(s) = s**2 + c*s + 1
-qp(s) = (s+1+sqrt((s+1)**2 - 4*rho(s)))/(2*rho(s))
-qm(s) = (s+1-sqrt((s+1)**2 - 4*rho(s)))/(2*rho(s))
+# qp(s) = (s+1+sqrt((s+1)**2 - 4*rho(s)))/(2*rho(s))
+# qm(s) = (s+1-sqrt((s+1)**2 - 4*rho(s)))/(2*rho(s))
+# d(q) = q**2*(c*q-1)**2 - 4*(q**2-q+1)*q**2
+# sp(q) = (-(c*q-1)*q + sqrt(d(q)))/(2*q**2)
+# sm(q) = (-(c*q-1)*q - sqrt(d(q)))/(2*q**2)
+qp(s) = (s+1+sqrt((s+1)**2 - 4*rho(s)))/(2*sqrt(rho(s)))
+qm(s) = (s+1-sqrt((s+1)**2 - 4*rho(s)))/(2*sqrt(rho(s)))
 d(q) = q**2*(c*q-1)**2 - 4*(q**2-q+1)*q**2
 sp(q) = (-(c*q-1)*q + sqrt(d(q)))/(2*q**2)
 sm(q) = (-(c*q-1)*q - sqrt(d(q)))/(2*q**2)
 
-#  = sqrt(s**2 + 2*cos(4*pi/5) + 1)
-# solplus(x) = x/2 + sqrt((x/2)**2 - 1)
-# solminus(x) = x/2 + sqrt((x/2)**2 - 1)
-# Tplus(s) = solplus((s+1)/rho(s))
-# Tminus(s) = solminus((s+1)/rho(s))
-# qinvp(s) = 0.5*(s+1+sqrt(2*s - 8*s*cos(2*pi/5) - 3*s**2 - 3))
-# qinvm(s) = 0.5*(s+1-sqrt(2*s - 8*s*cos(2*pi/5) - 3*s**2 - 3))
-# set trange [0:5]
-
-# sp(q) = (1-2*q*cos(2*pi/5)+sqrt((1-2*q*cos(2*pi/5))**2 - 4))/(2*q)
-# sm(q) = (1-2*q*cos(2*pi/5)-sqrt((1-2*q*cos(2*pi/5))**2 - 4))/(2*q)
-
 plot "output/barbot_map_5000_frequencies" \
-	 using ($1/100.0):($2/100.0):(($3==0)?1/0:$4) w p pt 5 ps 0.5 lc palette t '', \
+	 using ($1/100.0):($2/100.0*sqrt(rho($1/100.0))):(($3==0)?1/0:$4) w p pt 5 ps 0.5 lc palette t '', \
 	 "output/barbot_map_500000"	\
-	 using ($1/10.0) :($2/10.0) :($3*0.7+0.3) w p pt 7 ps variable lc 3 t '', \
-	 sm(t), d(t) > 0 ? t : 1/0 w l lw 2 lc 7 t "", \
-	 sp(t), d(t) > 0 ? t : 1/0 w l lw 2 lc 7 t "", \
+	 using ($1/10.0) :($2/10.0*sqrt(rho($1/10.0))) :($3*0.7+0.3) w p pt 7 ps variable lc 3 t '', \
+	 sm(t), d(t) > 0 ? t*sqrt(rho(sm(t))) : 1/0 w l lw 2 lc 7 t "", \
+	 sp(t), d(t) > 0 ? t*sqrt(rho(sp(t))) : 1/0 w l lw 2 lc 7 t "", \
 	 t, qm(t) w l lw 2 lc 7 t "", \
 	 t, qp(t) w l lw 2 lc 7 t ""
 
 # plot "output/barbot_map_50000_zoom_b" using ($1/1000.0):($2/5000):(($3==0)?1/0:$4) w p pt 5 ps 0.5 lc palette t ''
 
-pause mouse keypress
-reread
+# pause mouse keypress
+# reread