#include <Canvas\Canvas.mqh>

// Create canvas for drawing
   int width = 800;   // Canvas width
   int height = 600;  // Canvas height
   string canvas_name = "ButterflyCurve";
   
   // Create canvas object
   CCanvas canvas;
   if(!canvas.CreateBitmapLabel(canvas_name, 200, 50, width, height, COLOR_FORMAT_XRGB_NOALPHA))
     {
      Print("Error creating canvas: ", GetLastError());
      return;
     }

        // Set up drawing parameters
   int points = 1000;            // Number of points
   double t_start = 0;           // Start angle
   double t_end = 12 * M_PI;     // End angle
   double step = (t_end - t_start) / (points - 1);
   
   // Calculate curve points
   double x[], y[];
   ArrayResize(x, points);
   ArrayResize(y, points);
   
   for(int i = 0; i < points; i++)
     {
      double t = t_start + i * step;
      double expr = MathExp(MathCos(t)) - 2 * MathCos(4 * t) - MathPow(MathSin(t/12), 5);
      x[i] = MathSin(t) * expr;
      y[i] = MathCos(t) * expr;
     }

        // Find coordinate bounds for scaling
   double x_min = x[ArrayMinimum(x)];
   double x_max = x[ArrayMaximum(x)];
   double y_min = y[ArrayMinimum(y)];
   double y_max = y[ArrayMaximum(y)];
   
   // Scale points to canvas coordinates
   int x_px[], y_px[];
   ArrayResize(x_px, points);
   ArrayResize(y_px, points);
   
   double x_scale = (width - 40) / (x_max - x_min);
   double y_scale = (height - 40) / (y_max - y_min);
   double scale = MathMin(x_scale, y_scale); // Maintain aspect ratio
   
   for(int i = 0; i < points; i++)
     {
      x_px[i] = (int)((x[i] - x_min) * scale) + 20;
      y_px[i] = height - (int)((y[i] - y_min) * scale) - 20; // Flip Y-axis for canvas coordinates

       // Draw the curve
   canvas.Erase(ColorToARGB(clrWhite, 255)); // White background
   
   // Set line color - we'll pass this directly to Line() method
   uint line_color = ColorToARGB(clrBlue, 255);
   
   // Draw the polyline
   for(int i = 1; i < points; i++)
     {
      canvas.Line(x_px[i-1], y_px[i-1], x_px[i], y_px[i], line_color);
     }
   
   // Title
   canvas.FontSet("Arial", 20, FW_BOLD);
   canvas.TextOut(300, 20, "Butterfly Curve", ColorToARGB(clrBlack, 255));
   
   // Update display
   canvas.Update();

   //--- plot Butterfly
#property indicator_label1  "Butterfly Oscillator"
#property indicator_type1   DRAW_LINE
#property indicator_color1  DodgerBlue
#property indicator_width1  2
#property indicator_style1  STYLE_SOLID

//--- indicator levels
#property indicator_level1  2.5
#property indicator_level2 -2.5
#property indicator_level3  0.0

//--- input parameters
input bool   UsePriceStep = false; // Use ClosePrice as Step size for t increment
input double tmStep       = 0.05;  // Step size for t increment

double CalButterflyValue(int bar_index, double bar_close, double bar_open)
  {
   double tStep = UsePriceStep ? MathMod((bar_close - bar_open) / _Point, tmStep) : tmStep;
   double t = bar_index * tStep;

   // Butterfly curve formula
   double x = MathSin(t) *
              (MathExp(MathCos(t)) - 2.0 * MathCos(4.0 * t) - MathPow(MathSin(t / 12.0), 5));

   return (x);
  }

    int pStart = prev_calculated == 0 ? 0 : prev_calculated - 1;

   for(int i = pStart; i < rates_total; i++)
     {
      double bar_close = close[i];
      double bar_open  = open[i];
      ButterflyBuffer[i] = CalButterflyValue(i, bar_close, bar_open);
     }