      \setlength{\unitlength}{1cm}
      \footnotesize
      \DIVIDE{1}{12}{\invXII}
      \MULTIPLY{12}{\numberTWOPI}{\phione}
      \MULTIPLY{12}{64}{\divisions}

      \COMPOSITIONfunction{\EXPfunction}{\COSfunction}{\Afunction}
      \SCALEVARIABLEfunction{4}{\COSfunction}{\Bfunction}
      \SCALEVARIABLEfunction{\invXII}{\SINfunction}{\cfunction}
      \POWERfunction{\cfunction}{5}{\Cfunction}
      \LINEARCOMBINATIONfunction{1}{\Afunction}{-2}{\Bfunction}{\ABfunction}
      \SUMfunction{\ABfunction}{\Cfunction}{\ABCfunction}
      \PRODUCTfunction{\SINfunction}{\ABCfunction}{\Xfunction}
         % x=(sin t)(exp(cos t)-2 cos 4t + (sin(t/12))^5)
      \PRODUCTfunction{\COSfunction}{\ABCfunction}{\Yfunction}
         % y=(cos t)(exp(cos t)-2 cos 4t + (sin(t/12))^5)
      \PARAMETRICfunction{\Xfunction}{\Yfunction}{\butterfly}
      \centering
      \begin{Picture}(-4,-3)(4,4)
         \PlotParametricFunction[\divisions]\butterfly{0}{\phione}
      \end{Picture}
      \begin{gather*}
         x=\sin t\left(\mathrm e^{\cos t}-2\cos 4t
                      +\sin^5\left(\frac t{12}\right)\right) \\
         y=\cos t\left(\mathrm e^{\cos t}-2\cos 4t
                      +\sin^5\left(\frac t{12}\right)\right)
     \end{gather*}
