# Problems with ParametricPlot

I am trying to produce a diagram like this:

However, when I try to do it in Wolfram with this code:

f = -(34.91307692307692/Ω) +
0.5 √(4875.6917609467455/Ω^2 +
0.001183431952662722 (-2.10024854401*^11 - 15210. Ω^2) +
0.0003944773175542406 (2.10024854401*^11 +
15210. Ω^2) + (0.002485051380463261 \
(-6.502457060608313*^26 + 2.2360373408246284*^31 Ω^2 -
1.6195076985488275*^24 Ω^4 +
1.172847478703472*^17 Ω^6))/(Ω \
(1.6453401488537164*^57 Ω -
3.7717531641688455*^61 Ω^3 +
4.098352224227726*^54 Ω^5 +
2.967698194998834*^47 Ω^7 -
1.4328046927166397*^40 Ω^9 + \
√(3.498499802426748*^109 - 9.020035930925002*^113 Ω^2 -
6.4952975227022*^114 Ω^4 -
1.1355258747416519*^115 Ω^6 -
5.03883785494275*^112 Ω^8 -
5.03640596299178*^109 Ω^10 +
7.296556060973307*^102 Ω^12 -
2.6421768873633545*^95 Ω^14))^(1/3)) +
1/Ω 4.94066697104591*^-13 (1.6453401488537164*^57 \
Ω - 3.7717531641688455*^61 Ω^3 +
4.098352224227726*^54 Ω^5 +
2.967698194998834*^47 Ω^7 -
1.4328046927166397*^40 Ω^9 + \
√(3.498499802426748*^109 - 9.020035930925002*^113 Ω^2 -
6.4952975227022*^114 Ω^4 -
1.1355258747416519*^115 Ω^6 -
5.03883785494275*^112 Ω^8 -
5.03640596299178*^109 Ω^10 +
7.296556060973307*^102 Ω^12 -
2.6421768873633545*^95 Ω^14))^(1/3)) -
0.5 √(9751.383521893491/Ω^2 +
0.0015779092702169625 (-2.10024854401*^11 -
15210. Ω^2) - (0.002485051380463261 \
(-6.502457060608313*^26 + 2.2360373408246284*^31 Ω^2 -
1.6195076985488275*^24 Ω^4 +
1.172847478703472*^17 Ω^6))/(Ω \
(1.6453401488537164*^57 Ω -
3.7717531641688455*^61 Ω^3 +
4.098352224227726*^54 Ω^5 +
2.967698194998834*^47 Ω^7 -
1.4328046927166397*^40 Ω^9 + \
√(3.498499802426748*^109 - 9.020035930925002*^113 Ω^2 -
6.4952975227022*^114 Ω^4 -
1.1355258747416519*^115 Ω^6 -
5.03883785494275*^112 Ω^8 -
5.03640596299178*^109 Ω^10 +
7.296556060973307*^102 Ω^12 -
2.6421768873633545*^95 Ω^14))^(1/3)) -
1/Ω 4.94066697104591*^-13 (1.6453401488537164*^57 \
Ω - 3.7717531641688455*^61 Ω^3 +
4.098352224227726*^54 Ω^5 +
2.967698194998834*^47 Ω^7 -
1.4328046927166397*^40 Ω^9 + \
√(3.498499802426748*^109 - 9.020035930925002*^113 Ω^2 -
6.4952975227022*^114 Ω^4 -
1.1355258747416519*^115 Ω^6 -
5.03883785494275*^112 Ω^8 -
5.03640596299178*^109 Ω^10 +
7.296556060973307*^102 Ω^12 -
2.6421768873633545*^95 Ω^14))^(1/
3) + (0.25 (-(2.7236064240503376*^6/Ω^3) + \
(0.6610760127446518 (2.10024854401*^11 +
15210. Ω^2))/Ω - \
(6.311998221783861*^-8 (2.173675466865639*^18 +
3.10312759398801*^14 \
Ω^2))/Ω))/(√(4875.6917609467455/Ω^\
2 + 0.001183431952662722 (-2.10024854401*^11 - 15210. Ω^2) +
0.0003944773175542406 (2.10024854401*^11 +
15210. Ω^2) + (0.002485051380463261 \
(-6.502457060608313*^26 + 2.2360373408246284*^31 Ω^2 -
1.6195076985488275*^24 Ω^4 +
1.172847478703472*^17 Ω^6))/(Ω \
(1.6453401488537164*^57 Ω -
3.7717531641688455*^61 Ω^3 +
4.098352224227726*^54 Ω^5 +
2.967698194998834*^47 Ω^7 -
1.4328046927166397*^40 Ω^9 + \
√(3.498499802426748*^109 - 9.020035930925002*^113 Ω^2 -
6.4952975227022*^114 Ω^4 -
1.1355258747416519*^115 Ω^6 -
5.03883785494275*^112 Ω^8 -
5.03640596299178*^109 Ω^10 +
7.296556060973307*^102 Ω^12 -
2.6421768873633545*^95 Ω^14))^(1/3)) +
1/Ω 4.94066697104591*^-13 (1.6453401488537164*^57 \
Ω - 3.7717531641688455*^61 Ω^3 +
4.098352224227726*^54 Ω^5 +
2.967698194998834*^47 Ω^7 -

1.4328046927166397*^40 Ω^9 + \
√(3.498499802426748*^109 - 9.020035930925002*^113 Ω^2 -
6.4952975227022*^114 Ω^4 -
1.1355258747416519*^115 Ω^6 -
5.03883785494275*^112 Ω^8 -
5.03640596299178*^109 Ω^10 +
7.296556060973307*^102 Ω^12 -
2.6421768873633545*^95 Ω^14))^(1/3))))

ParametricPlot[{Re[f],Im[f/(2*Pi)]},{Ω,Pi,20Pi}]


I get only this:

I already checked the evaluation of the function comparing its values versus Matlab (where the figure comes from) and it is correct. My question is: How can I correct the commands of the ParametricPlot in order to obtain the desired figure?.

• Maybe add AspectRatio->1 or AspectRatio->1/GoldenRatio? Apr 23, 2019 at 15:56
• @CarlWoll: I already tried what your recommend, unfortunately it did not work. Apr 23, 2019 at 16:14
• It seems like your function pretty rapidly oscillates between +1763 and -1763 (or thereabouts). The imaginary part does not seem to evaluate to a positive number at 1.1 Pi or 1.2 Pi as well as many other values of Omega. Apr 23, 2019 at 17:53

ParametricPlot[{Re[f], Abs[Im[f]/(2*Pi)]}, {\[CapitalOmega], Pi,
`