Here is a simple program that I use to teach computational physics to non-programmers. It's an n-body code which uses a vortex kernel in 2D to draw lines. The initial positions and strength are set to generate a fuzzy, growing spirograph-like wreath in the middle of the screen.

1. // vortex - advanced version
   // Mark J Stock
   // me@markjstock.com
   
   // use this many particles
   int num = 400;
   // this variable scales how fast everything moves
   float dt = 2.0;
   
   // these arrays store the parameters for each particle
   float[] x = new float[num];
   float[] y = new float[num];
   float[] s = new float[num];
   
   // this gets run only once, before any iteration begins
   void setup() {
     size(1280, 960);
    
     for (int i=0; i<num; i=i+1) {
       // create the particles randomly in the middle of the screen
       //x[i] = random(100, 540);
       //y[i] = random(100, 380);
       // or, create them along a circle
       float rad = height/3.5;
       float theta = i*2.0*3.1415927/num;
       x[i] = width/2.0 + rad*sin(theta);
       y[i] = height/2.0 + rad*cos(theta);
       // here we set the strength, centered on zero
       s[i] = random(-1, 1);
     }
    
     frameRate(60);
     background(50);
   }
   
   // this gets called once for each frame
   void draw() {
    
     // turn off outlines
     noStroke();
    
     // set the color for all particles
     // four numbers are: red, green, blue, alpha/transparency
     // each covers a range from 0 to 255
     fill(255, 255, 255, 12);
   
     // loop over the vortex particles
     for (int i=0; i<num; i=i+1) {
      
       // compute the new velocity of each particle
       float velx = 0.0;
       float vely = 0.0;
       for (int j=0; j<num; j=j+1) {
         // particle j affects particle i's speed based on
         //   a function of the distance and the direction
         //   between the two particles
         float dx = x[j] - x[i];
         float dy = y[j] - y[i];
         // the 1.0 here is a smoothing parameter
         float distsq = dx*dx + dy*dy + 1.0;
         // this kernel looks like attraction/repulsion
         //velx = velx + s[j]*dx/distsq;
         //vely = vely + s[j]*dy/distsq;
         // this kernel looks like fluid dynamics
         velx = velx - s[j]*dy/distsq;
         vely = vely + s[j]*dx/distsq;
       }
      
       // move each particle according to its new velocity
       x[i] = x[i] + dt*velx;
       y[i] = y[i] + dt*vely;
   
       // and draw each particle as a 2x2 pixel circle
       ellipse(x[i], y[i], 2.0, 2.0);
     }
   }
   
   void keyPressed() {
     if (key == 'p') {
       saveFrame("img_vortex_#####.png");
     }
   }