Fractal series

gistfile1.js

function rnorm(mean, sd){
  if (mean === undefined){
    mean = 0;
  }
  if (sd === undefined){
    sd = 1;
  }

  do {
    var x1 = 2.0 * Math.random() - 1.0;
    var x2 = 2.0 * Math.random() - 1.0;
    var w = x1 * x1 + x2 * x2;
  } while (w >= 1.0);
  w = Math.sqrt( -2.0 * Math.log(w) / w);
  
  return x1 * w * sd + mean;
}

function rcauchy(){
  var n1 = rnorm();
  var n2 = rnorm();

  while (n2 == 0.0){
    n2 = rnorm();
  }

  return n1 / n2;
}

function fract(arr, sd, a, b, depth){
  if (a >= b - 1 || depth <= 0){
    return;
  }

  var breakpoint = Math.random();
  var mid = Math.floor(breakpoint * (b - a) + a);

  if (mid == a){
    mid++;
    breakpoint = (mid - a) / (b - a);
  }

  var r;
  switch(document.getElementById("method").value){
  case "uniform":
    r = (Math.random() - 0.5) * sd * Math.sqrt(12);
    break;
  case "gaussian":
    r = rnorm() * sd;
    break;
  case "cauchy":
    r = rcauchy() * sd;
    break;
  }

  arr[mid] = (arr[b] - arr[a]) / (b - a) * (mid - a) + arr[a];
  arr[mid] += Math.floor(r);

  fract(arr, sd, a, mid, depth - 1);
  fract(arr, sd, mid, b, depth - 1);

  return;
}

function draw(){
  var cvs = document.getElementById("canvas");
  var ctx = cvs.getContext("2d");

  var n = 500;
  var arr = new Array(n);
  arr[0]  = parseInt(document.getElementById("start").value);
  arr[n - 1] = parseInt(document.getElementById("end").value);

  var sd = parseFloat(document.getElementById("sd").value);

  fract(arr, sd, 0, n - 1, 100);

  ctx.fillStyle = "white";
  ctx.fillRect(0, 0, 500, 500);

  // draw the series
  ctx.beginPath();
  ctx.strokeStyle = "black";
  ctx.moveTo(0, arr[0]);
  for (var i = 1; i < n; i++){
    if (arr[i] != undefined){
      ctx.lineTo(i, arr[i]);
    }
  }
  ctx.stroke();

  // draw average values
  ctx.beginPath();
  ctx.strokeStyle = "red";
  ctx.moveTo(0, arr[0]);
  var sum = arr[0];
  for (var i = 1; i < n; i++){
    if (arr[i] != undefined){
      sum += arr[i];
      ctx.lineTo(i, Math.floor(sum / (i + 1)));
    }
  }
  ctx.stroke();
}