My inspiration of this project is from my first time experience of using processing—to build an application for visualizing Smith chart to help myself learning electromagnetic theory. When I think of generative art or animation by code, I always think about math. Therefore, I draw  Cardioid learned in high school on paper and envision something like water wave or magnetic field… I try the equations on processing. And try to make some change of the equation. Finally I use this equation:

y=a*(3*cos(rad)-cos(3*rad));
x=a*(3*sin(rad)-sin(3*rad));

Next,  I make the curves move out to intimate magnetic field. Finally,  I tried 3D function to render the curves. After trials, I found white line reduce the sense of 3D but seems more harmony in the image.

 
int     nFramesInLoop = 10; 
int     nElapsedFrames;
boolean bRecording; 

String myName="wanfangdiao";
//===================================================
void setup() {
  size (1500, 1500,P3D); 

  bRecording = false;
  nElapsedFrames = 0;
  frameRate (nFramesInLoop); 
}
//===================================================
void keyPressed() { 
  // Press a key to export frames to the output folder
  bRecording = true;
  nElapsedFrames = 0;
}

//===================================================
void draw() {
// Compute a percentage (0...1) representing where we are in the loop.
  float percentCompleteFraction = 0; 
  if (bRecording) {
    percentCompleteFraction = (float) nElapsedFrames / (float)nFramesInLoop;
  } 
  else {
    float modFrame = (float) (frameCount % nFramesInLoop);
    percentCompleteFraction = modFrame / (float)nFramesInLoop;
  }

  // Render the design, based on that percentage. 
  renderMyDesign (percentCompleteFraction);

  // If we're recording the output, save the frame to a file. 
  if (bRecording) {
    saveFrame("output/"+ myName + "-loop-" + nf(nElapsedFrames, 4) + ".png");
    nElapsedFrames++; 
    if (nElapsedFrames == nFramesInLoop) {
      bRecording = false;
    }
  }
}

//===================================================
void renderMyDesign (float percent) {
 background(255);
 strokeWeight(2);
 //smooth();
 for(int i=0; i<= 200; i+=20)
 {
drawCardioid(percent*2, i);
 }

}

void drawCardioid (float change, int startpoint)
{
float a=startpoint+10*change;
int centerX=750;
int centerY=750;
//
//stroke(0,30);
//noFill();

stroke(255);
float x, y;
float lastx=-2999;
float lasty=-2999;
for(float t=0; t <= 360; t+=5){
  pushMatrix();
float rad=radians(t);

y=centerY-a*(3*cos(rad)-cos(3*rad));
x=centerX+a*(3*sin(rad)-sin(3*rad));
translate(x,y,0);
rotateZ(0.5);
fill(100,0,200,50);
box(40);
 popMatrix();

}

}