dominiccooney/index.html

## index.html
<!DOCTYPE html>
<style>
canvas {
  width: 1000px;
  height: 1000px;
  background: black;
}
</style>
<canvas width="1000" height="1000"></canvas>
<script>
'use strict';

// Generates a random number uniformly distributed between 0 and n-1.
function uniformInt(n) {
  return Math.floor(Math.random() * n);
}

// Generates a uniformly distributed angle, in radians.
function uniformAngle() {
  return 2 * Math.PI * Math.random();
}

const epsilon = 1e-16;

function standardNormal() {
  standardNormal.generate = !standardNormal.generate;
  if (standardNormal.generate) {
    // There's a cached result.
    return standardNormal.y;
  }

  do {
   var u = Math.random();
   var v = uniformAngle();
  } while (u < Number.MIN_VALUE);

  let factor = Math.sqrt(-2 * Math.log(u));
  let x = factor * Math.cos(v);
  standardNormal.y = factor * Math.sin(v);
  return x;
}

standardNormal.generate = true;

function clip(min, max, value) {
  return Math.max(min, Math.min(max, value));
}

let width = 1000;
let height = 1000;

function Walk() {
  this.xs = [uniformInt(width)];
  this.ys = [uniformInt(height)];
}

Walk.prototype.draw = function(c) {
  c.beginPath();
  c.moveTo(this.xs[0], this.ys[0]);
  for (let i = 1; i < this.xs.length; i++) {
    c.lineTo(this.xs[i], this.ys[i]);
  }
  c.stroke();
}

// A random walk with a uniformly distributed step size.
function RandomWalk(stepSize) {
  Walk.call(this);
  this.stepSize = stepSize;
}

RandomWalk.prototype = Object.create(Walk.prototype);

RandomWalk.prototype.step = function() {
  let dir = uniformAngle();
  let dist = Math.random() * this.stepSize;
  this.xs.push(
      clip(0, width, this.xs[this.xs.length - 1] + Math.cos(dir) * dist));
  this.ys.push(
      clip(0, height, this.ys[this.ys.length - 1] + Math.sin(dir) * dist));
};

// A Levy flight.
function LevyFlight(stepSize) {
  Walk.call(this);
  this.stepSize = stepSize;

  // See Yang, X.-S., Nature-Inspired Optimization Algorithms, p. 50.
  this.beta = 3/2;

  // From http://stackoverflow.com/questions/15454183/how-to-make-a-function-that-computes-the-factorial-for-numbers-with-decimals
  function gamma(z) {
    return Math.sqrt(2 * Math.PI / z) * Math.pow((1 / Math.E) * (z + 1 / (12 * z - 1 / (10 * z))), z);
  }

  // I have some doubt that this is correct because the denominator is zero
  // for beta=1 which should correspond to the Cauchy distribution.
  this.sigmaU = gamma(1 + this.beta) * Math.sin(Math.PI * this.beta / 2) /
                (gamma((1 + this.beta) / 2) * this.beta *
                 Math.pow(2, (this.beta - 1) / 2));
  this.sigmaU = Math.pow(this.sigmaU, 1 / this.beta);
  this.sigmaV = 1;
}

LevyFlight.prototype = Object.create(Walk.prototype);

LevyFlight.prototype.step = function() {
  let dir = uniformAngle();
  let u = standardNormal() * this.sigmaU * this.stepSize;
  let v = standardNormal() * this.sigmaV * this.stepSize;
  let dist = u / Math.pow(Math.abs(v), 1 / this.beta);
  this.xs.push(
      clip(0, width, this.xs[this.xs.length - 1] + Math.cos(dir) * dist));
  this.ys.push(
      clip(0, height, this.ys[this.ys.length - 1] + Math.sin(dir) * dist));
};

var canvas = document.querySelector('canvas');
var c = canvas.getContext('2d');
c.clearRect(0, 0, c.canvas.width, c.canvas.height);

// Draw a random walk.
var walk = new RandomWalk(20);
for (let i = 0; i < 1000; i++) {
  walk.step();
}
c.strokeStyle = 'skyblue';
walk.draw(c);

// Draw a Levy flight.
var flight = new LevyFlight(20);
for (let i = 0; i < 1000; i++) {
  flight.step();
}
c.strokeStyle = 'red';
flight.draw(c);
</script>
	<!DOCTYPE html>
	<style>
	canvas {
	width: 1000px;
	height: 1000px;
	background: black;
	}
	</style>
	<canvas width="1000" height="1000"></canvas>
	<script>
	'use strict';

	// Generates a random number uniformly distributed between 0 and n-1.
	function uniformInt(n) {
	return Math.floor(Math.random() * n);
	}

	// Generates a uniformly distributed angle, in radians.
	function uniformAngle() {
	return 2 * Math.PI * Math.random();
	}

	const epsilon = 1e-16;

	function standardNormal() {
	standardNormal.generate = !standardNormal.generate;
	if (standardNormal.generate) {
	// There's a cached result.
	return standardNormal.y;
	}

	do {
	var u = Math.random();
	var v = uniformAngle();
	} while (u < Number.MIN_VALUE);

	let factor = Math.sqrt(-2 * Math.log(u));
	let x = factor * Math.cos(v);
	standardNormal.y = factor * Math.sin(v);
	return x;
	}

	standardNormal.generate = true;

	function clip(min, max, value) {
	return Math.max(min, Math.min(max, value));
	}

	let width = 1000;
	let height = 1000;

	function Walk() {
	this.xs = [uniformInt(width)];
	this.ys = [uniformInt(height)];
	}

	Walk.prototype.draw = function(c) {
	c.beginPath();
	c.moveTo(this.xs[0], this.ys[0]);
	for (let i = 1; i < this.xs.length; i++) {
	c.lineTo(this.xs[i], this.ys[i]);
	}
	c.stroke();
	}

	// A random walk with a uniformly distributed step size.
	function RandomWalk(stepSize) {
	Walk.call(this);
	this.stepSize = stepSize;
	}

	RandomWalk.prototype = Object.create(Walk.prototype);

	RandomWalk.prototype.step = function() {
	let dir = uniformAngle();
	let dist = Math.random() * this.stepSize;
	this.xs.push(
	clip(0, width, this.xs[this.xs.length - 1] + Math.cos(dir) * dist));
	this.ys.push(
	clip(0, height, this.ys[this.ys.length - 1] + Math.sin(dir) * dist));
	};

	// A Levy flight.
	function LevyFlight(stepSize) {
	Walk.call(this);
	this.stepSize = stepSize;

	// See Yang, X.-S., Nature-Inspired Optimization Algorithms, p. 50.
	this.beta = 3/2;

	// From http://stackoverflow.com/questions/15454183/how-to-make-a-function-that-computes-the-factorial-for-numbers-with-decimals
	function gamma(z) {
	return Math.sqrt(2 * Math.PI / z) * Math.pow((1 / Math.E) * (z + 1 / (12 * z - 1 / (10 * z))), z);
	}

	// I have some doubt that this is correct because the denominator is zero
	// for beta=1 which should correspond to the Cauchy distribution.
	this.sigmaU = gamma(1 + this.beta) * Math.sin(Math.PI * this.beta / 2) /
	(gamma((1 + this.beta) / 2) * this.beta *
	Math.pow(2, (this.beta - 1) / 2));
	this.sigmaU = Math.pow(this.sigmaU, 1 / this.beta);
	this.sigmaV = 1;
	}

	LevyFlight.prototype = Object.create(Walk.prototype);

	LevyFlight.prototype.step = function() {
	let dir = uniformAngle();
	let u = standardNormal() * this.sigmaU * this.stepSize;
	let v = standardNormal() * this.sigmaV * this.stepSize;
	let dist = u / Math.pow(Math.abs(v), 1 / this.beta);
	this.xs.push(
	clip(0, width, this.xs[this.xs.length - 1] + Math.cos(dir) * dist));
	this.ys.push(
	clip(0, height, this.ys[this.ys.length - 1] + Math.sin(dir) * dist));
	};

	var canvas = document.querySelector('canvas');
	var c = canvas.getContext('2d');
	c.clearRect(0, 0, c.canvas.width, c.canvas.height);

	// Draw a random walk.
	var walk = new RandomWalk(20);
	for (let i = 0; i < 1000; i++) {
	walk.step();
	}
	c.strokeStyle = 'skyblue';
	walk.draw(c);

	// Draw a Levy flight.
	var flight = new LevyFlight(20);
	for (let i = 0; i < 1000; i++) {
	flight.step();
	}
	c.strokeStyle = 'red';
	flight.draw(c);
	</script>