Harmonograph in 3D

// Harmonograph

// by Steven Kay

// 6-pendulum formula, 2 pendulums per axis (x,y,z)

// 

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float f1,f2,f3,f4,f5,f6; //frequencies

float fscale=20.0;

​

float p1,p2,p3,p4,p5,p6; //phase shifts

float pscale=TWO_PI;

​

float a1,a2,a3,a4,a5,a6; //amplitudes

float ascale=1.0;

​

float k=220.0; //SIZE

float E=2.71828; // 

float damping=0.001; // increase to make figure shrink over size, e.g 0.1 or 0.01

​

float tstart=0.0;

​

int LENGTH=200; // length of trail in boxes

int SIZE=20; // size of largest box

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void setup() {

  size(512,512,P3D);

  background(0);

  color(255);

  fill(255);

  reset();

}

​

void mousePressed() {

  reset();

}

​

void draw() {

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  background(0);

  float step=.01; // gap between boxes

  float damp=k*pow(E,-damping*tstart); // damping

​

  camera(0.0,0.0,500.0,0.0,0.0,0.0,0.0,-1.0,0.0);

  // tumble

  rotateX(radians(frameCount%360));

  rotateZ(radians(frameCount%360));

  // draw trails

  for (int i=0;i<LENGTH;i++) {

    float t=tstart+(step*(float)i);    

    float x=damp*(a1*sin(f1*t + p1) + a2*sin(f2*t + p2)); 

    float y=damp*(a3*sin(f3*t + p3) + a4*sin(f4*t + p4)); 

    float z=damp*(a5*cos(f5*t + p5) + a6*cos(f6*t + p6));

    float pc=(float)i/LENGTH;

    float op=pc*255.0; //color

    fill(op);

    pushMatrix();

      translate(x,y,z);

      box(pc*SIZE,pc*SIZE,pc*SIZE);

    popMatrix();

  }

  tstart+=step;

}

​

void reset(){

  // 

  tstart=0.0;

  // frequencies

  f1=random(0,1.0)*fscale;

  f2=random(0,1.0)*fscale;

  f3=random(0,1.0)*fscale;

  f4=random(0,1.0)*fscale;

  f5=random(0,1.0)*fscale;

  f6=random(0,1.0)*fscale;

  // phase angles

  p1=random(0,1.0)*pscale;

  p2=random(0,1.0)*pscale;

  p3=random(0,1.0)*pscale;

  p4=random(0,1.0)*pscale;

  p5=random(0,1.0)*pscale;

  p6=random(0,1.0)*pscale;

  // amplitudes

  a1=random(0,1.0)*ascale;

  a2=random(0,1.0)*ascale;

  a3=random(0,1.0)*ascale;

  a4=random(0,1.0)*ascale;

  a5=random(0,1.0)*ascale;

  a6=random(0,1.0)*ascale;

}

​