Fibonacci Spiral

Posted on March 28th, 2010 in Code Sketches. No Comments.

I am fascinated by the Fibonacci (Golden) Spiral, and love the geometric construction, which is mimicked and expanded in this Processing sketch.

While developing an earlier concept for my website redesign, I created this version of the Fibonacci Spiral, with subtle coloration and fading arcs and squares. Make sure you stare at it for a little while to see the change!

// large version
// second attempt at a fibonacci spiral
// first attempt was great, but used rotation,
// which is expensive and imprecise
// here's the beginning of the fibonacci sequence...
// 0, 1, 1, 2, 3, 5, 8

void setup() {
  size(611, 378);
  smooth();
  frameRate(30);
}

int[] s = new int[3];
int tmp, phase;
float speed;

void draw() {
  // clear the screen to a nice green
  background(228, 236, 215);
  
  // initialize variables
  s[0] = 0;
  s[1] = 0; // first number of the fibonacci sequence
  s[2] = 1; // second number of the fibonacci sequence
  phase = 0; // simple counter; use this to apply fx to the boxes linearly
  speed = 0.01; // speed of the effects

  // set the origin at the end of the spiral
  translate(442, 272);
  
  // flip vertically to match my logo
  scale(1.0, -1.0);
  
  rotate(PI);

  // this loop constructs the spiral
  // basically, draw a square of side s, rotate 90deg, calculate the new s0 and s,
  // move up s0 + s, and repeat...
  while (s[2] < 611) {

    // use a sin function to give us some nice undulating effects
    float wave = sin((frameCount + phase*20) * speed) + 1.0;
    
    // styles for the arcs
    fill(0, 0, wave * 64, 10); // undulating transparent black fill
    stroke(255, wave * 255); // undulating white stroke

    // draw the quarter-circles inside the squares
    // set the stroke weight to 2 for the arc that makes the spiral
    if (phase % 4 == 0) strokeWeight(2); else strokeWeight(1);
    arc(s[2], s[2], 2*s[2], 2*s[2], PI, 3*PI/2.0);
    if (phase % 4 == 1) strokeWeight(2); else strokeWeight(1);
    arc(0, s[2], 2*s[2], 2*s[2], -PI/2.0, 0);
    if (phase % 4 == 2) strokeWeight(2); else strokeWeight(1);
    arc(0, 0, 2*s[2], 2*s[2], 0, PI/2.0);
    if (phase % 4 == 3) strokeWeight(2); else strokeWeight(1);
    arc(s[2], 0, 2*s[2], 2*s[2], PI/2.0, PI);
    
    // styles for the squares
    noFill();
    stroke(255, 255, 255, 255);
    strokeWeight(1);

    // draw the square
    rect(0, 0, s[2], s[2]);
    
    // calculate the next number in the fibonacci sequence
    tmp = s[2];
    s[2] += s[1];
    s[0] = s[1];
    s[1] = tmp;
    
    // translate to get in position for the next square
    switch(phase % 4) {
      case 0:
        translate(s[1], 0);
      break;
      case 1:
        translate(-s[0], s[1]);
      break;
      case 2:
        translate(-s[2], -s[0]);
      break;
      case 3:
        translate(0, -s[2]);
      break;
    }
    
    phase++;
  }
}

Φ