//Butterfly curve.
//Bourke, P. "Butterfly Curve." http://astronomy.swin.edu.au/~pbourke/curves/butterfly/. 

#include <vector>

Double_t x_fun(Double_t t)
{
   using namespace TMath;
   return Sin(t) * (Exp(Cos(t)) - 2 * Cos(4 * t) + Power(Sin(1 / 12. * t), 5));
   //return 1.3 * TMath::Cos(t);//ellipse
}

Double_t y_fun(Double_t t)
{
   using namespace TMath;
   return Cos(t) * (Exp(Cos(t)) - 2 * Cos(4 * t) + Power(Sin(1 / 12. * t), 5));
   //return TMath::Sin(t);//ellipse
}

void param()
{
   const Double_t tMin = 0., tMax = 15 * TMath::TwoPi();
   const Int_t nPoints = 2000;
   const Double_t step = (tMax - tMin) / (nPoints - 1);
   std::vector<Double_t> xArr(nPoints), yArr(nPoints);

   for(Int_t i = 0; i < nPoints; ++i)
   {
      xArr[i] = x_fun(tMin + i * step);
      yArr[i] = y_fun(tMin + i * step);
   }

   TGraph *graph = new TGraph(nPoints, &xArr[0], &yArr[0]);
   graph->SetLineColor(kRed);
   TCanvas *c = new TCanvas("parametric", "parametric", 100, 100, 400, 400);
   c->Range(-4.5, -4.5, 4.5, 4.5);
   graph->Draw();
}