// By progressively subdividing it into 

// a 3-gon, 6-gon, 12-gon, 24-gon, etc., 

// with smooth interpolations.

// Golan Levin, January 2017

​

var radius;

var trianglePoints = [];

var nCirclePoints = 3;

var period = 2500;

var nPows = 5;

​

//-----------------------------------------

function setup() {

  createCanvas(400, 400);

  radius = width / 2 * 0.75;

}

​

//-----------------------------------------

function draw() {

  background(255);

  push();

  translate(width / 2, height / 2);

​

  var t = int(millis() / period); // 0,1,2,3,4,5,6,7...

  var tupow = 3 * floor(pow(2, 0 + (t % nPows))); // 3,6,12,24,48...

  var utpow = 3 * floor(pow(2, 0 + (nPows - (t % nPows) - 1))); // 48,24,12,6,3...

  print(tupow + " " + utpow);

  var direction = (int(millis() / (period * nPows))) % 2; // 0,1,0,1...

  var bitupow = (direction === 0) ? tupow : utpow; // 

​

  var frac = (millis() % period) / float(period);

  var tfrac = (direction === 0) ? frac : (1.0 - frac);

  tfrac = pow(tfrac, 3.0);

​

  noFill();

  stroke(0);

  strokeWeight(3);

  strokeJoin(MITER);

​

  beginShape();

  nCirclePoints = 2 * bitupow; 

  for (var i = 0; i <= (nCirclePoints + 1); i++) { // for good shape closure

    if (i % 2 === 0) {

      // the corner vertices

      var theta = map(i, 0, nCirclePoints, 0, TWO_PI)  - HALF_PI;

      var px = radius * cos(theta);

      var py = radius * sin(theta);

      vertex(px, py);

​

    } else {

      // the halfway vertices

      var thetaA = map(i - 1, 0, nCirclePoints, 0, TWO_PI) - HALF_PI;

      var thetaB = map(i + 0, 0, nCirclePoints, 0, TWO_PI) - HALF_PI;

      var thetaC = map(i + 1, 0, nCirclePoints, 0, TWO_PI) - HALF_PI;

​

      var pxA = radius * cos(thetaA);

      var pyA = radius * sin(thetaA);

      var pxB = radius * cos(thetaB);

      var pyB = radius * sin(thetaB);

      var pxC = radius * cos(thetaC);

      var pyC = radius * sin(thetaC);

​

      var pxAC = (pxA + pxC) / 2; // points halfway between flanking vertices

      var pyAC = (pyA + pyC) / 2;

​

      var px = map(tfrac, 0, 1, pxAC, pxB);

      var py = map(tfrac, 0, 1, pyAC, pyB);

      vertex(px, py);

    }

  }

  endShape(CLOSE);

​

  pop();

}

​