up to vector folds, missing cosfunc

folds/folds.pde

@@ -0,0 +1,79 @@
+void setup() {
+  size(600, 600);
+  background(0);
+  smooth(8);
+  noFill();
+  stroke(250, 15);
+  strokeWeight(0.9);
+ 
+  x1=y1=-3;
+  x2=y2=3;
+  y=y1;
+  step=(x2-x1)/(2.321*width);
+}
+ 
+float x1, y1, x2, y2; // function domain
+float step; // step within domain
+float y;
+ 
+boolean go = true;
+void draw() {
+  if (go) {
+    for (int i=0; (i<20)&go; i++) { // draw 20 lines at once
+      for (float x=x1; x<=x2; x+=step) {
+        drawVariation(x, y);
+      }
+      y+=step;
+      if (y>y2) {
+        go = false;
+        println("done");
+        //save("pdj + hyperbolic * pdj.png");
+      }
+    }
+  }
+}
+ 
+void drawVariation(float x, float y) {
+  PVector v = new PVector(x, y);
+  float amount = 2.0;
+  v = addF(pdj(v,amount),mulF(hyperbolic(v,amount),pdj(v,amount)));
+  
+  //wrapping
+  v.x = (v.x - x1) % (x2-x1);
+  if(v.x<0) v.x += (x2-x1);
+  v.y = (v.y - y1) % (y2-y1);
+  if(v.y<0) v.y += (y2-y1);
+  v.x += x1;
+  v.y += y1;
+  
+  float xx = map(v.x+0.003*randomGaussian(), x1, x2, 20, width-20);
+  float yy = map(v.y+0.003*randomGaussian(), y1, y2, 20, height-20);
+  point(xx, yy);
+}
+
+PVector sinusoidal(PVector v, float amount) {
+  return new PVector(amount * sin(v.x), amount * sin(v.y));
+}
+
+PVector hyperbolic(PVector v, float amount) {
+  float r = v.mag() + 1.0e-10;
+  float theta = atan2(v.x, v.y);
+  float x = amount * sin(theta) / r;
+  float y = amount * cos(theta) * r;
+  return new PVector(x, y);
+}
+
+// parametrization P={pdj_a,pdj_b,pdj_c,pdj_d}
+float pdj_a = 0.4;
+float pdj_b = 1.23;
+float pdj_c = -0.3;
+float pdj_d = -1.98;
+PVector pdj(PVector v, float amount) {
+  return new PVector( amount * (sin(pdj_a * v.y) - cos(pdj_b * v.x)),
+                      amount * (sin(pdj_c * v.x) - cos(pdj_d * v.y)));
+}
+
+PVector addF(PVector v1, PVector v2) { return new PVector(v1.x+v2.x, v1.y+v2.y); }
+PVector subF(PVector v1, PVector v2) { return new PVector(v1.x-v2.x, v1.y-v2.y); }
+PVector mulF(PVector v1, PVector v2) { return new PVector(v1.x*v2.x, v1.y*v2.y); }
+PVector divF(PVector v1, PVector v2) { return new PVector(v2.x==0?0:v1.x/v2.x, v2.y==0?0:v1.y/v2.y); }

vector_field/vector_field.pde

@@ -0,0 +1,62 @@
+// dynamic list with our points, PVector holds position
+ArrayList<PVector> points = new ArrayList<PVector>();
+ 
+// colors used for points
+color[] pal = {
+  color(0, 91, 197),
+  color(0, 180, 252),
+  color(23, 249, 255),
+  color(223, 147, 0),
+  color(248, 190, 0)
+};
+ 
+// global configuration
+float vector_scale = 0.01; // vector scaling factor, we want small steps
+float time = 0; // time passes by
+ 
+void setup() {
+  size(800, 800);
+  strokeWeight(0.66);
+  background(0, 5, 25);
+  noFill();
+  smooth(8);
+ 
+  // noiseSeed(1111); // sometimes we select one noise field
+ 
+  // create points from [-3,3] range
+  for (float x=-3; x<=3; x+=0.07) {
+    for (float y=-3; y<=3; y+=0.07) {
+      // create point slightly distorted
+      PVector v = new PVector(x+randomGaussian()*0.003, y+randomGaussian()*0.003);
+      points.add(v);
+    }
+  }
+}
+ 
+void draw() {
+  int point_idx = 0; // point index
+  for (PVector p : points) {
+    // map floating point coordinates to screen coordinates
+    float xx = map(p.x, -6.5, 6.5, 0, width);
+    float yy = map(p.y, -6.5, 6.5, 0, height);
+ 
+    // select color from palette (index based on noise)
+    int cn = (int)(100*pal.length*noise(point_idx))%pal.length;
+    stroke(pal[cn], 15);
+    point(xx, yy); //draw
+ 
+    // placeholder for vector field calculations
+    float n = TWO_PI * noise(p.x,p.y);
+    PVector v = new PVector(n,n);
+ 
+    // v is vector from the field
+    //PVector v = new PVector(0.1, 0.1);
+ 
+    p.x += vector_scale * v.x;
+    p.y += vector_scale * v.y;
+ 
+    // go to the next point
+    point_idx++;
+  }
+  time += 0.001;
+}