function to_pair(z) {

  let s = sqrt(8*z + 1);

  let w = floor( (s - 1) / 2 );

  let t = w * (w + 1) / 2;

  let y = z - t;

  let x = w - y;

  return [x, y];

}

​

// Cantor's pairing function

function from_pair(x, y) {

  return (x + y + 1) * (x + y) / 2 + y;

}

​

// OEIS A277577

let next_n = function() {

  let a = 0, b = 0, c = 0, d = -1, n = -1;

  return function() {

    while(true) {

      c = c > 0 ? c - 1 : a++;

      if(d < b)  d++;

      else { d = 0; b++; }

      n++;

      if(0 < c && c < d && (c + d) % 2) {

        return n;

      }

    }

  }

}();

​

function pythag_triple(n, m) {

  let m2 = m*m, n2 = n*n;

  return [ m2 - n2, 2*m*n, m2 + n2];

}

​

function closest_triple(x, y) {

  let m = (abs(x) + sqrt(x*x + y*y)) / 2;

  m = round(sqrt(m));

  let n = round( abs(y)/(2 * m) );

  return pythag_triple(n, m);

}

​

function circle_div(r, n) {

  let a = 2*PI/n;

  let b = 0;

  stroke("darkred");

  strokeWeight(0.5);

  circle(width/2, height/2, r*2);

  strokeWeight(2);

  while(b < 2*PI) {

    let x = r*cos(b);

    let y = r*sin(b);

    b = b + a;

    strokeWeight(0.5);

    line(width/2 + x, height/2 - y, width/2, height/2);

  }

}

​

let scale = 1;

let radius = 2000;

​

function mouseClicked() {

  let x = (mouseX - width/2) / scale;

  let y = (height/2 - mouseY) / scale;

  let t = closest_triple(x, y);

  x = x/abs(x) * t[0];

  y = y/abs(y) * t[1];

  print(x, y);

  let ang = atan2(y,x);

  x = radius * cos(ang);

  y = radius * sin(ang);

  stroke("green");

  line(width/2,height/2, width/2+x, height/2-y);

}

​

function setup() {

  noLoop();

  createCanvas(8200, 4200);

  background(0);

  strokeWeight(2);

  noFill();

  scrollTo((width - windowWidth)/2, 

           (height - windowHeight)/2);

  let tri = 31;

  let max = tri*(tri+1)/2;

  let u = 1, v = 1, w = 3;

  point(width/2 + 0, height/2 - 0);

  for(let i = 0; i < max; i++) {

    let j = next_n();

    let k = to_pair(j);

    let t = pythag_triple(...k);

    let [a, b, c] = t;

    [a, b, c] = [a*scale, b*scale, c*scale];

    stroke("white");

    point(width/2 + a, height/2 - b);

    point(width/2 - a, height/2 - b);

    point(width/2 - a, height/2 + b);

    point(width/2 + a, height/2 + b);

    if(v == 0) {

      v = u = u + 1;

      stroke("white");

      point(width/2 + w*w*scale, height/2);

      point(width/2 - w*w*scale, height/2);

      w = w + 2;

    }

    v = v - 1;

  }

  stroke("white");

  point(width/2 + w*w*scale, height/2);

  point(width/2 - w*w*scale, height/2);

​

  circle_div(radius*scale, 60);

}

​

function draw() {

}