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Leveraging web workers

Building on information presented in Enabling touch, here we discuss how to improve performance by using Web Workers.

Note  A webpage page that uses Web Workers must be served via the HTTP or HTTPS protocol.

As described in Web Workers, the Web Worker API provides a way for web application authors to spawn background scripts that run in parallel (concurrently) with the main page. You can spawn several threads at a time to use for long-running tasks. A new worker object requires a .js file, which is included via an asynchronous request to the web server.


var myWorker = new Worker('worker.js');

All communication to and from the worker thread is managed through messages. Both the host worker and the worker script can send messages by using postMessage, and listen for a response by using the onmessage event. The content of the message is sent as the data property of the event object.

With this understanding in place, the algorithm is:

  1. In the main page (user interface) thread, place the information necessary to generate a Mandelbrot image (in the form of a canvas data array) into an object literal.
  2. Using postMessage, send the object literal to the worker thread for processing.
  3. When the worker thread has completed its processing, the finished canvas image data array is sent back to the user interface (UI) thread, where it's displayed on the canvas.

To accommodate this algorithm, drawMandelbrot is modified as follows:


function drawMandelbrot(ReMax, ReMin, ImMax, ImMin, grayscaleFactor) {      
  var startTime = new Date(); // Report how long it takes to render this particular region of the Mandelbrot set.             
  var messageBox = document.getElementById('messageBox');     
  var elapsedTime =  document.getElementById('elapsedTime');     
  var canvas = globals.canvas; // A small speed optimization - accessing local variables tends to be faster than accessing global variables.
  var canvasWidth = canvas.width;
  var canvasHeight = canvas.height;
  var ctx = canvas.context;  
  var imageDataObject = ctx.imageDataObject; // imageDataObject ends up receiving an altered copy of ctx.imageDataObject, so imageDataObject is not a pointer to (reference to) ctx.imageDataObject.
  var maxPixelGrayscaleValue = 0; // This will contain the lightest shade of gray in the drawn Mandelbrot image.
  var fineDetailMandelbrotReceived = false; // Just in case the fine detail Web Worker callback finishes before the coarse detail Web Worker callback.

  messageBox.innerHTML = "Calculating..."; // This isn't displayed until the drawMandelbrot function block exits.
  elapsedTime.innerHTML = ""; // Erase the prior run's statistics.
          
  var workerMessage = {
    workerID: "",
    MAX_ITERATIONS: MAX_ITERATIONS,
    ReMax: ReMax,
    ReMin: ReMin,
    ImMax: ImMax,
    ImMin: ImMin,
    grayscaleFactor: grayscaleFactor,
    canvasWidth: canvasWidth,
    canvasHeight: canvasHeight,
    imageDataObject: imageDataObject
  };
  
  function workerCallback(evt) { // Receive the required data from the Web Worker to draw the Mandelbrot set to the canvas (plus a few other items).          
    if (fineDetailMandelbrotReceived) {
      return; // For some reason, the fine detail callback finished before the coarse detail callback - do not display the coarse Mandelbrot image.
    }
    
    ctx.putImageData(evt.data.imageDataObject, 0, 0); // Render our carefully constructed canvas image data array to the canvas.
    globals.canvas.context.imageDataObject = evt.data.imageDataObject; 
    globals.maxPixelGrayscaleValue = evt.data.maxPixelGrayscaleValue; // Store this information in case the user clicks the Lighten button.          
  
    var elapsedMilliseconds = (new Date()) - startTime;
    elapsedTime.innerHTML = evt.data.workerID + ": " + evt.data.iterationSum.format() + " iterations in " + (elapsedMilliseconds / 1000).toFixed(2) + " seconds"; // Note that the UI element is not updated until after this block terminates (which is the desired behavior).            
    
    if (evt.data.workerID == "Fine detail") {
      fineDetailMandelbrotReceived = true;
      messageBox.innerHTML = DEFAULT_MESSAGE; // Erase the "Calculating..." message and replace it with the default message.
    } // if
  } // workerCallback
  
  globals.coarseDetailWorker.onmessage = workerCallback; // I unnecessarily set this callback each time drawMandelbrot is called - this is fine in that there's no significant performance hit.
  globals.fineDetailWorker.onmessage = workerCallback;

  workerMessage.MAX_ITERATIONS = Math.round(MAX_ITERATIONS / 2); // MAX_ITERATIONS must always been a (positive) integer.
  workerMessage.workerID = "Coarse detail";
  globals.coarseDetailWorker.postMessage(workerMessage); // postMessage to the coarse detail Web Worker. 

  workerMessage.MAX_ITERATIONS = MAX_ITERATIONS;
  workerMessage.workerID = "Fine detail";                
  globals.fineDetailWorker.postMessage(workerMessage); // postMessage to the fine detail Web Worker.
} // drawMandelbrot

Because a worker thread has no access to the DOM (and cannot, in general, receive objects that reference the DOM), we place the information necessary to generate a Mandelbrot image into an object literal. This object literal is sent from the UI thread to the worker thread:


var workerMessage = {
  workerID: "",
  MAX_ITERATIONS: MAX_ITERATIONS,
  ReMax: ReMax,
  ReMin: ReMin,
  ImMax: ImMax,
  ImMin: ImMin,
  grayscaleFactor: grayscaleFactor,
  canvasWidth: canvasWidth,
  canvasHeight: canvasHeight,
  imageDataObject: imageDataObject
};

The imageDataObject object provides the canvas image data array that is to be filled in by the worker thread.

With this information understood, Mandelbrot 8 is presented next:

Mandelbrot 8


<!DOCTYPE html>
<html>

<head>
  <meta http-equiv="X-UA-Compatible" content="IE=10" />
  <meta content="text/html; charset=utf-8" http-equiv="Content-Type">
  <title>Mandelbrot 8</title>
  <style>
    html, body {
      margin: 0;
      padding: 0;
      text-align: center;
    }
    
    canvas {
      border: 2px solid black;
      -ms-touch-action: none;
      touch-action: none; /* Use the standard, if available. */
    }    
    
    table {
      margin: 0 auto; /* Center the table. */
    }
    
    #messageBox {
      text-align: left;
    }
        
    #elapsedTime {
      width: 23em;
      text-align: right;
    }    

    button {
      width: 5em;
    }
    
    #filenameForm {
      visibility: hidden; /* As opposed to "display: none", keep room for this hidden element in the layout. */
    }
}
  </style>      
</head>

<body>
  <h1>Mandelbrot 8</h1>
  <table>
    <tr>
      <td id="messageBox"></td>
      <td id="elapsedTime"></td>
    </tr>
  </table>
  <canvas width="600" height="400" oncontextmenu="return false;"> <!-- Because the hold gesture event can fire more than once, the 'oncontextmenu="return false;"' attribute is used to stop the right-click context menu from appearing inappropriately. -->
    Canvas not supported - upgrade your browser (after checking that your browser is in the correct mode).
  </canvas><br>
  <button type="button" id="resetButton">Reset</button>  
  <button type="button" id="lightenButton">Lighten</button>    
  <button type="button" id="saveButton">Save</button>
  <form id="filenameForm"> 
    Extensionless filename: <input id="filename" type="text"> <input type="submit" value="Submit">
  </form>
  <script>
    if (!window.Worker) { // Check for the availability of the Worker() constructor.
      document.getElementsByTagName('body')[0].innerHTML = "<h2>Web Workers not supported - upgrade your browser<br>(after checking that your browser is in the correct mode)</h2>";      
    }
    else {
      var RE_MAX = 1.1; // This value will be adjusted as necessary to ensure that the rendered Mandelbrot set is never skewed (that is, true to it's actual shape).
      var RE_MIN = -2.5;
      var IM_MAX = 1.2;
      var IM_MIN = -1.2;
      var MAX_ITERATIONS = 1200; // Increase this value to improve detection of complex c values that belong to the Mandelbrot set.
      var STATIC_ZOOM_BOX_FACTOR = 0.25; // Increase to make the double-click and hold gesture zoom box bigger.
      var DEFAULT_MESSAGE = "Click or click-and-drag to zoom."      
      
      var globals = {}; // See the handleLoad function.
      
      window.addEventListener('load', handleLoad, false);
    } // if-else
                
    /************************************************************************************************************************************************************/
    
    Number.prototype.format = function() {
    /* 
      Formats this integer so that it has commas in the expected places.
    */
    	var numberString = Math.round(this).toString(); // An integer value is assumed, so we ensure that it is indeed an integer.
    	var precompiledRegularExpression = /(\d+)(\d{3})/;
    	
    	while ( precompiledRegularExpression.test(numberString) ) {
    		numberString = numberString.replace(precompiledRegularExpression, '$1' + ',' + '$2'); // For this integer, inject ","'s at the appropriate locations.
    	} // while
    	
    	return numberString;
    } // Number.prototype.format

    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/    

    function handleLoad() {          
      var canvas = document.getElementsByTagName('canvas')[0];
      var canvasWidth = canvas.width;
      var canvasHeight = canvas.height;      
      var ctx = canvas.getContext('2d');
      
      document.getElementsByTagName('table')[0].width = canvasWidth; // Make the table's width the same as the canvas's width. 
      document.getElementById('messageBox').innerHTML = DEFAULT_MESSAGE;            

      globals.canvas = canvas;
      globals.canvas.context = ctx;
      globals.canvas.context.imageDataObject = ctx.createImageData(canvasWidth, canvasHeight); // Create an appropriately sized but empty canvas image data object.
      
      globals.staticZoomBoxWidth = STATIC_ZOOM_BOX_FACTOR * canvasWidth; // Maintains the original canvas width/height ratio.
      globals.staticZoomBoxHeight = STATIC_ZOOM_BOX_FACTOR * canvasHeight; // Maintains the original canvas width/height ratio.      
      
      globals.pointer = {};
      globals.pointer.down = false;  
                 
      window.addEventListener('hashchange', handleHashChange, false); // This event handler executes whenever the URL hash string changes.
      
      if (window.navigator.pointerEnabled || window.navigator.msPointerEnabled) { // Future proofing.
        // It's either-or with MS pointer events - they cannot be registered concurrently.
        window.gesture = window.gesture || window.MSGesture; // Future proofing.
        globals.gesture = new gesture();
        globals.gesture.target = canvas; 
        canvas.addEventListener('MSPointerDown', function(evt) { globals.gesture.addPointer(evt.pointerId); }, false); 
          
        canvas.addEventListener('MSGestureStart', handlePointer, false); 
        canvas.addEventListener('mousedown', handlePointer, false); // Required for the case when the mouse is clicked but not moved.
        
        canvas.addEventListener('MSGestureChange', handlePointer, false);
        
        canvas.addEventListener('MSGestureEnd', handlePointer, false);
        canvas.addEventListener('mouseup', handlePointer, false); // Required for the case when the mouse is clicked but not moved.

        canvas.addEventListener('MSGestureHold', handlePointer, false);
      }    
      else {
        canvas.addEventListener('mousedown', handlePointer, false);
        canvas.addEventListener('mousemove', handlePointer, false);
        canvas.addEventListener('mouseup', handlePointer, false);    
      } // if-else
            
      document.getElementById('resetButton').addEventListener('click', handleResetButton, false);
      document.getElementById('lightenButton').addEventListener('click', handleLightenButton, false);    
      document.getElementById('saveButton').addEventListener('click', handleSaveButton, false);        
      document.getElementById('filenameForm').addEventListener('submit', handleFormSubmit, false);    
      
      ctx.fillStyle = "rgba(255, 0, 0, 0.3)"; // The color and opacity of the zoom box. This is what gets saved when calling ctx.save().          
 
      handleHashChange(); // On page load, simulate a page URL change to draw the initial Mandelbrot set.
    } // handleLoad
    
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/    
    
    function handleHashChange() {
      var hashValues = getHashValues(); // This function examines window.location.hash but doesn't change it.
      
      if (hashValues) {
        globals.ReMax = hashValues.ReMax;
        globals.ReMin = hashValues.ReMin;
        globals.ImMax = hashValues.ImMax;
        globals.ImMin = hashValues.ImMin;
        globals.grayscaleFactor = hashValues.grayscaleFactor;
      }
      else {
        globals.ReMax = adjusted_RE_MAX();
        globals.ReMin = RE_MIN;
        globals.ImMax = IM_MAX;
        globals.ImMin = IM_MIN;     
        globals.grayscaleFactor = 1; // Multiplying any value by 1 has no effect.
      } // if-else
      
      initializeWebWorkers('mandelbrotWebWorker.js'); // Halt any in-process Web Workers so that the back/forward buttons behave as expected (i.e., deal with the asynchronous nature of the Web Workers).
      drawMandelbrot(globals.ReMax, globals.ReMin, globals.ImMax, globals.ImMin, globals.grayscaleFactor);
    } // handelHashChange    

    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/        

    function getHashValues() {
      var dirtyComplexPlaneExtremaString = (window.location.hash).replace('#', ''); // Remove the leading "#" character from the string.
      var complexPlaneExtremaString = dirtyComplexPlaneExtremaString.split(','); // Returns an array. Assumes the following string form: "ReMax,ReMin,ImMax,ImMin,grayscaleFactor" (note that if grayscaleFactor is 1, the image's grayscale is not affected).
      
      var ReMax = parseFloat( complexPlaneExtremaString[0] ); 
      var ReMin = parseFloat( complexPlaneExtremaString[1] ); 
      var ImMax = parseFloat( complexPlaneExtremaString[2] ); 
      var ImMin = parseFloat( complexPlaneExtremaString[3] );
      var grayscaleFactor = parseFloat( complexPlaneExtremaString[4] );
      
      if ( isNaN(ReMax) || isNaN(ReMin) || isNaN(ImMax) || isNaN(ImMin) || isNaN(grayscaleFactor) ) { 
        return null;
      } // if 
      
      return {ReMax: ReMax, ReMin: ReMin, ImMax: ImMax, ImMin: ImMin, grayscaleFactor: grayscaleFactor};
    } // getHashValues
        
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/        

    function adjusted_RE_MAX() {    
      var ReMax = globals.canvas.width * ( (IM_MAX - IM_MIN) / globals.canvas.height ) + RE_MIN;
      
      if (RE_MAX != ReMax) {
        alert("RE_MAX has been adjusted to: " + ReMax); // The user should never see this if RE_MAX is set correctly above.
      } // if

      return ReMax;
    } // adjusted_RE_MAX    
    
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/    
    
    function drawMandelbrot(ReMax, ReMin, ImMax, ImMin, grayscaleFactor) {      
      var startTime = new Date(); // Report how long it takes to render this particular region of the Mandelbrot set.             
      var messageBox = document.getElementById('messageBox');     
      var elapsedTime =  document.getElementById('elapsedTime');     
      var canvas = globals.canvas; // A small speed optimization - accessing local variables tends to be faster than accessing global variables.
      var canvasWidth = canvas.width;
      var canvasHeight = canvas.height;
      var ctx = canvas.context;  
      var imageDataObject = ctx.imageDataObject; // imageDataObject ends up receiving an altered copy of ctx.imageDataObject, so imageDataObject is not a pointer to (reference to) ctx.imageDataObject.
      var maxPixelGrayscaleValue = 0; // This will contain the lightest shade of gray in the drawn Mandelbrot image.
      var fineDetailMandelbrotReceived = false; // Just in case the fine detail Web Worker callback finishes before the coarse detail Web Worker callback.

      messageBox.innerHTML = "Calculating..."; // This isn't displayed until the drawMandelbrot function block exits.
      elapsedTime.innerHTML = ""; // Erase the prior run's statistics.
              
      var workerMessage = {
        workerID: "",
        MAX_ITERATIONS: MAX_ITERATIONS,
        ReMax: ReMax,
        ReMin: ReMin,
        ImMax: ImMax,
        ImMin: ImMin,
        grayscaleFactor: grayscaleFactor,
        canvasWidth: canvasWidth,
        canvasHeight: canvasHeight,
        imageDataObject: imageDataObject
      };
      
      function workerCallback(evt) { // Receive the required data from the Web Worker to draw the Mandelbrot set to the canvas (plus a few other items).          
        if (fineDetailMandelbrotReceived) {
          return; // For some reason, the fine detail callback finished before the coarse detail callback - do not display the coarse Mandelbrot image.
        }
        
        ctx.putImageData(evt.data.imageDataObject, 0, 0); // Render our carefully constructed canvas image data array to the canvas.
        globals.canvas.context.imageDataObject = evt.data.imageDataObject; 
        globals.maxPixelGrayscaleValue = evt.data.maxPixelGrayscaleValue; // Store this information in case the user clicks the Lighten button.          
      
        var elapsedMilliseconds = (new Date()) - startTime;
        elapsedTime.innerHTML = evt.data.workerID + ": " + evt.data.iterationSum.format() + " iterations in " + (elapsedMilliseconds / 1000).toFixed(2) + " seconds"; // Note that the UI element is not updated until after this block terminates (which is the desired behavior).            
        
        if (evt.data.workerID == "Fine detail") {
          fineDetailMandelbrotReceived = true;
          messageBox.innerHTML = DEFAULT_MESSAGE; // Erase the "Calculating..." message and replace it with the default message.
        } // if
      } // workerCallback
      
      globals.coarseDetailWorker.onmessage = workerCallback; // I unnecessarily set this callback each time drawMandelbrot is called - this is fine in that there's no significant performance hit.
      globals.fineDetailWorker.onmessage = workerCallback;

      workerMessage.MAX_ITERATIONS = Math.round(MAX_ITERATIONS / 2); // MAX_ITERATIONS must always been a (positive) integer.
      workerMessage.workerID = "Coarse detail";
      globals.coarseDetailWorker.postMessage(workerMessage); // postMessage to the coarse detail Web Worker. 

      workerMessage.MAX_ITERATIONS = MAX_ITERATIONS;
      workerMessage.workerID = "Fine detail";                
      globals.fineDetailWorker.postMessage(workerMessage); // postMessage to the fine detail Web Worker.
    } // drawMandelbrot
    
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/
    
    function xToRe(x) {
      var x_coefficient = (globals.ReMax - globals.ReMin) / globals.canvas.width; 
      
      return (x * x_coefficient) + globals.ReMin; // Converts a canvas x-coordinate value to the associated complex plane Re-coordinate.
    } // xToRe
    
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/    

    function yToIm(y) {
      var y_coefficient = (globals.ImMin - globals.ImMax) / globals.canvas.height; 
      
      return (y * y_coefficient) + globals.ImMax; // Converts a canvas y-coordinate value to the associated complex plane Im-coordinate.
    } // yToIm
    
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/

    function handlePointer(evt) {
      var canvasWidthHeightRatio = globals.canvas.width / globals.canvas.height;
      var ctx = globals.canvas.context;
      
      var canvasX;
      var canvasY;      
      
      if (evt.offsetX && evt.offsetY) {
        canvasX = evt.offsetX; // Not supported in Firefox.
        canvasY = evt.offsetY; // Does not assume that the canvas element is a direct descendent of the body element.
      } else {
        canvasX = evt.clientX - evt.target.offsetLeft; // Supported in Firefox.
        canvasY = evt.clientY - evt.target.offsetTop; // Assumes that the canvas element is a direct descendent of the body element.
      } // if-else
      
      var zoomBoxWidth;
      var zoomBoxHeight;
      
      var ReMax;
      var ReMin;
      var ImMax;
      var ImMin;
      
      var staticZoomBoxWidth = globals.staticZoomBoxWidth;
      var staticZoomBoxHeight = globals.staticZoomBoxHeight;
      var halfStaticZoomBoxWidth = staticZoomBoxWidth / 2;
      var halfStaticZoomBoxHeight = staticZoomBoxHeight / 2;
      
      switch (evt.type) {
        case 'MSGestureStart':              
        case 'mousedown':
          globals.pointer.down = true;      
          globals.pointer.x1 = canvasX;
          globals.pointer.y1 = canvasY;
          break;
        case 'MSGestureChange':                  
        case 'mousemove':
          if (globals.pointer.down) {
            zoomBoxHeight = Math.abs(canvasY - globals.pointer.y1);  
            zoomBoxWidth = zoomBoxHeight * canvasWidthHeightRatio; // We must keep the zoom box dimensions proportional to the canvas dimensions in order to ensure that the resulting zoomed Mandelbrot image does not become skewed.
            ctx.putImageData(ctx.imageDataObject, 0, 0); // Assumes that an initial image of the Mandelbrot set is drawn before we get to this point in the code. The purpose of this line is to erase the prior zoom box rectangle before drawing the next zoom box rectangle.
            ctx.fillRect(globals.pointer.x1, globals.pointer.y1, zoomBoxWidth, zoomBoxHeight); // With a freshly painted image of the current Mandelbrot set in place (see prior line), draw a new zoom box rectangle.
          }
          break;
        case 'MSGestureEnd':
        case 'mouseup':
          globals.pointer.down = false;          
          
          zoomBoxHeight = Math.abs(canvasY - globals.pointer.y1); // Only allow the zoom box to be drawn from an upper-left corner position down to a lower-right corner position.
          zoomBoxWidth = zoomBoxHeight * canvasWidthHeightRatio; // Again, ensure that the width/height ratio of the zoom box is proportional to the canvas's (this simplifies the algorithm).          
          
          if (zoomBoxHeight == 0) { // No zoom box has been drawn, so honor the fixed sized zoom box.  
            ctx.putImageData(ctx.imageDataObject, 0, 0); // For the MSGestureHold case, erase the previously drawn zoom box so we don't draw two or more on top of each other.
            ctx.fillRect(canvasX - halfStaticZoomBoxWidth, canvasY - halfStaticZoomBoxHeight, staticZoomBoxWidth, staticZoomBoxHeight); // Just leave this on the screen.
                         
            ReMin = xToRe(canvasX - halfStaticZoomBoxWidth); // Center the static zoom box about the point (evt.offsetX, evt.offsetY).
            ImMax = yToIm(canvasY - halfStaticZoomBoxHeight); 
            
            ReMax = xToRe(canvasX + halfStaticZoomBoxWidth);
            ImMin = yToIm(canvasY + halfStaticZoomBoxHeight);
          } 
          else { // A (possibly tiny) zoom box has been drawn, so honor it.
            ReMin = xToRe(globals.pointer.x1); // Convert the mouse's x-coordinate value (on the canvas) to the associated Re-coordinate value in the complex plane.
            ImMax = yToIm(globals.pointer.y1); // Convert the mouse's y-coordinate value (on the canvas) to the associated Im-coordinate value in the complex plane.
                                      
            ReMax = xToRe(zoomBoxWidth + globals.pointer.x1); // Convert the zoom box's final x-coordinate value to the associated Re-coordinate value in the complex plane.  
            ImMin = yToIm(zoomBoxHeight + globals.pointer.y1);  // Convert the zoom box's final y-coordinate value to the associated Re-coordinate value in the complex plane.            
          } // if-else        
        
          window.location.hash = ReMax + "," + ReMin + "," + ImMax + "," + ImMin + "," + globals.grayscaleFactor; // This triggers the handleHashChange event handler which, among other things, is responsible for drawing the Mandelbrot set.
          break; 
        case 'MSGestureHold':
          if (evt.detail & evt.MSGESTURE_FLAG_BEGIN) {
            ctx.fillRect(canvasX - halfStaticZoomBoxWidth, canvasY - halfStaticZoomBoxHeight, staticZoomBoxWidth, staticZoomBoxHeight); // At the first sign of a hold gesture, get the zoom box up on the screen immediately.                 
          }  
          
          // The evt.MSGESTURE_FLAG_END component of the hold gesture is handled by the "if (zoomBoxHeight == 0)" clause of the MSGestureEnd clause above.
          
          break;
        default:
          alert("Error in switch statement."); // Although unnecessary, defensive programming techniques such as this are highly recommended.
      } // switch              
    } // handlePointer    
    
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/
    
    function handleResetButton() {
      window.location.hash = adjusted_RE_MAX() + "," + RE_MIN + "," + IM_MAX + "," + IM_MIN + "," + 1; // // This triggers the handleHashChange event handler which, among other things, is responsible for drawing the Mandelbrot set.
    } // handleResetButton
    
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/
    
    function handleLightenButton() {
    /* 
      This creates a value (factor) such that black (0) stays black and the lightest gray value in the image becomes white (255). Thus, clicking the 
      Lighten button can remove mathematical meaning of the (proper) grayscale but can make dark images more visible.
    */
      var grayscaleFactor = 255 / globals.maxPixelGrayscaleValue; // For the canvas element, 255 is white, 0 is black.

      window.location.hash = globals.ReMax + "," + globals.ReMin + "," + globals.ImMax + "," + globals.ImMin + "," + grayscaleFactor; // This invokes handleHashChange which, among other things, is responsibile for drawing the Mandelbrot set.
    } // handleResetButton
    
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/

    function handleSaveButton() {
      document.getElementById('filenameForm').style.visibility = "visible";
      document.getElementById('filename').focus(); // Place the cursor in the filename text input box.
    } // handleResetButton 
 
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/

    function handleFormSubmit(evt) {
    /* 
      As of 8/2012, the following code only works starting with Internet Explorer 10.
    */
      evt.preventDefault(); // Do not refresh the page when the Submit button is clicked.
      
      window.BlobBuilder = window.BlobBuilder || window.MSBlobBuilder || window.WebKitBlobBuilder || window.MozBlobBuilder;
      globals.canvas.toBlob = globals.canvas.toBlob || globals.canvas.msToBlob;      
      window.navigator.saveBlob = window.navigator.saveBlob || window.navigator.msSaveBlob;
      
      if (window.BlobBuilder && globals.canvas.toBlob && window.navigator.saveBlob) {
        var extensionlessFilename = evt.target[0].value;
        var filename = extensionlessFilename + ".png";
        var blobBuilderObject = new BlobBuilder(); // Create a blob builder object so that we can append content to it.
                
        blobBuilderObject.append( globals.canvas.toBlob() ); // Append the user's drawing in PNG format to the builder object.
        window.navigator.saveBlob(blobBuilderObject.getBlob(), filename); // Move the builder object content to a blob and save it to a file.      
      }
      else {
        document.getElementById('messageBox').innerHTML = "<strong style='color: red;'>CANNOT SAVE FILE</strong>";
      } // if-else
      
      document.getElementById('filenameForm').style.visibility = "hidden";
    } // handleFormSubmit

    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/

    function initializeWebWorkers(webWorkerJsPath) {
      if (globals.coarseDetailWorker) {
        globals.coarseDetailWorker.terminate();      
      }
      
      if (globals.fineDetailWorker) {
        globals.fineDetailWorker.terminate();      
      }
      
      globals.coarseDetailWorker = new Worker(webWorkerJsPath);
      globals.fineDetailWorker = new Worker(webWorkerJsPath);
    } // initializeWebWorkers
  </script>
</body>

</html>

To start, if Web Workers are not available, we say so and halt. Otherwise, we initialize as before:


if (!window.Worker) { // Check for the availability of the Worker() constructor.
  document.getElementsByTagName('body')[0].innerHTML = "<h2>Web Workers not supported - upgrade your browser<br>(after checking that your browser is in the correct mode)</h2>";      
}
else {
  var RE_MAX = 1.1; // This value will be adjusted as necessary to ensure that the rendered Mandelbrot set is never skewed (that is, true to it's actual shape).
  var RE_MIN = -2.5;
  var IM_MAX = 1.2;
  var IM_MIN = -1.2;
  var MAX_ITERATIONS = 1200; // Increase this value to improve detection of complex c values that belong to the Mandelbrot set.
  var STATIC_ZOOM_BOX_FACTOR = 0.25; // Increase to make the double-click and hold gesture zoom box bigger.
  var DEFAULT_MESSAGE = "Click or click-and-drag to zoom."      
  
  var globals = {}; // See the handleLoad function.
  
  window.addEventListener('load', handleLoad, false);
} // if-else

In handleHashChange, we invoke initializeWebWorkers('mandelbrotWebWorker.js'). The mandelbrotWebWorker.js file defines the code to be executed by the worker threads. The initializeWebWorkers function, itself, is shown next:


function initializeWebWorkers(webWorkerJsPath) {
  if (globals.coarseDetailWorker) {
    globals.coarseDetailWorker.terminate();      
  }
  
  if (globals.fineDetailWorker) {
    globals.fineDetailWorker.terminate();      
  }
  
  globals.coarseDetailWorker = new Worker(webWorkerJsPath);
  globals.fineDetailWorker = new Worker(webWorkerJsPath);
} // initializeWebWorkers

The two if statements are used to terminate a possibly in-process worker thread, which is necessary if the user clicks the back or forward button before the current Mandelbrot image is fully rendered.

The last two lines create two global variables containing two identical worker objects (that is, they both execute the same code residing at webWorkerJsPath).

When the page loads, handleLoad is executed, which invokes handleHashChange. handleHashChange invokes initializeWebWorkers('mandelbrotWebWorker.js') (as described above) followed by drawMandelbrot, which has been modified to invoke two concurrent worker threads as follows:


function drawMandelbrot(ReMax, ReMin, ImMax, ImMin, grayscaleFactor) {      
  var startTime = new Date(); // Report how long it takes to render this particular region of the Mandelbrot set.             
  var messageBox = document.getElementById('messageBox');     
  var elapsedTime =  document.getElementById('elapsedTime');     
  var canvas = globals.canvas; // A small speed optimization - accessing local variables tends to be faster than accessing global variables.
  var canvasWidth = canvas.width;
  var canvasHeight = canvas.height;
  var ctx = canvas.context;  
  var imageDataObject = ctx.imageDataObject; // imageDataObject ends up receiving an altered copy of ctx.imageDataObject, so imageDataObject is not a pointer to (reference to) ctx.imageDataObject.
  var maxPixelGrayscaleValue = 0; // This will contain the lightest shade of gray in the drawn Mandelbrot image.
  var fineDetailMandelbrotReceived = false; // Just in case the fine detail Web Worker callback finishes before the coarse detail Web Worker callback.

  messageBox.innerHTML = "Calculating..."; // This isn't displayed until the drawMandelbrot function block exits.
  elapsedTime.innerHTML = ""; // Erase the prior run's statistics.
          
  var workerMessage = {
    workerID: "",
    MAX_ITERATIONS: MAX_ITERATIONS,
    ReMax: ReMax,
    ReMin: ReMin,
    ImMax: ImMax,
    ImMin: ImMin,
    grayscaleFactor: grayscaleFactor,
    canvasWidth: canvasWidth,
    canvasHeight: canvasHeight,
    imageDataObject: imageDataObject
  };
  
  function workerCallback(evt) { // Receive the required data from the Web Worker to draw the Mandelbrot set to the canvas (plus a few other items).          
    if (fineDetailMandelbrotReceived) {
      return; // For some reason, the fine detail callback finished before the coarse detail callback. Don't display the coarse Mandelbrot image.
    }
    
    ctx.putImageData(evt.data.imageDataObject, 0, 0); // Render our carefully constructed canvas image data array to the canvas.
    globals.canvas.context.imageDataObject = evt.data.imageDataObject; 
    globals.maxPixelGrayscaleValue = evt.data.maxPixelGrayscaleValue; // Store this information in case the user clicks the Lighten button.          
  
    var elapsedMilliseconds = (new Date()) - startTime;
    elapsedTime.innerHTML = evt.data.workerID + ": " + evt.data.iterationSum.format() + " iterations in " + (elapsedMilliseconds / 1000).toFixed(2) + " seconds"; // Note that the UI element is not updated until after this block terminates (which is the desired behavior).            
    
    if (evt.data.workerID == "Fine detail") {
      fineDetailMandelbrotReceived = true;
      messageBox.innerHTML = DEFAULT_MESSAGE; // Erase the "Calculating..." message and replace it with the default message.
    } // if
  } // workerCallback
  
  globals.coarseDetailWorker.onmessage = workerCallback; // I unnecessarily set this callback each time drawMandelbrot is called - this is fine in that there's no significant performance hit.
  globals.fineDetailWorker.onmessage = workerCallback;

  workerMessage.MAX_ITERATIONS = Math.round(MAX_ITERATIONS / 2); // MAX_ITERATIONS must always been a (positive) integer.
  workerMessage.workerID = "Coarse detail";
  globals.coarseDetailWorker.postMessage(workerMessage); // postMessage to the coarse detail Web Worker. 

  workerMessage.MAX_ITERATIONS = MAX_ITERATIONS;
  workerMessage.workerID = "Fine detail";                
  globals.fineDetailWorker.postMessage(workerMessage); // postMessage to the fine detail Web Worker.
} // drawMandelbrot

Skipping the workerCallback callback function for now, the drawMandelbrot function next executes the following lines:


globals.coarseDetailWorker.onmessage = workerCallback; // I unnecessarily set this callback each time drawMandelbrot is called - this is fine in that there's no significant performance hit.
globals.fineDetailWorker.onmessage = workerCallback;

workerMessage.MAX_ITERATIONS = Math.round(MAX_ITERATIONS / 2); // MAX_ITERATIONS must always be a (positive) integer.
workerMessage.workerID = "Coarse detail";
globals.coarseDetailWorker.postMessage(workerMessage); // postMessage to the coarse detail Web Worker. 

workerMessage.MAX_ITERATIONS = MAX_ITERATIONS;
workerMessage.workerID = "Fine detail";                
globals.fineDetailWorker.postMessage(workerMessage); // postMessage to the fine detail Web Worker.

That is, and for both worker objects, we specify the callback function (workerCallback) to be executed when a worker thread returns a message, in the form of an object literal, to the UI thread.

Next, we set the empty workerID value in order to later determine which object literal came from what worker.

Finally, we post the previously constructed workerMessage object literal messages to the worker threads for processing. These two messages are received by the (DOM-unaware) worker thread code:

mandelbrotWebWorker.js


/* 
  Recall that a Web Worker JavaScript file has no access to the DOM and, in general, cannot receive DOM related objects.  
*/

self.onmessage = function(evt) {
  var MAX_ITERATIONS = evt.data.MAX_ITERATIONS;
  var ReMax = evt.data.ReMax;
  var ReMin = evt.data.ReMin;
  var ImMax = evt.data.ImMax;
  var ImMin = evt.data.ImMin;
  var grayscaleFactor = evt.data.grayscaleFactor;
  var canvasWidth = evt.data.canvasWidth;
  var canvasHeight = evt.data.canvasHeight;
  var imageDataObject = evt.data.imageDataObject; // This is a copy of, not a reference to, globals.canvas.context.imageDataObject.
  
  var imageDataObjectData = imageDataObject.data; // As a performance optimization, we cache this data array.
  var maxPixelGrayscaleValue = 0; // This will contain the lightest shade of gray in the drawn Mandelbrot image.
  
  var x_coefficient = (ReMax - ReMin) / canvasWidth; // Keep the below loops as computation-free as possible.
  var y_coefficient = (ImMin - ImMax) / canvasHeight; // Keep the below loops as computation-free as possible.
  
  var iterationSum = 0;
  var currentPixel = 0;  
  for (var y = 0; y < canvasHeight; y++) {
    var c_Im = (y * y_coefficient) + ImMax; // Note that c = c_Re + c_Im*i
    
    for (var x = 0; x < canvasWidth; x++) {
      var c_Re = (x * x_coefficient) + ReMin // Convert the canvas x-coordinate to a complex plane Re-coordinate. c_Re represents the real part of a c value.
      
      var z_Re = 0; // The first z value (Zo) must be 0.
      var z_Im = 0; // The first z value (Zo) must be 0. Note that z = z_Re + z_Im*i
      
      var c_belongsToMandelbrotSet = true; // Assume that the c associated with Zn belongs to the Mandelbrot set (i.e., Zn remains bounded under iteration of Zn+1 = (Zn)^2 + c).
      var exponentialSmoothingSum = 0; // Used to color the c-value pixels that are not part of the Mandelbrot set (i.e., tend toward infinity under iteration of Zn+1 = (Zn)^2 + c).
      for (var iterationCount = 1; iterationCount <= MAX_ITERATIONS; iterationCount++) {
        iterationSum++; // Keep track of how many iterations were performed in total so we can report this to the user.
      
        var z_Re_squared = z_Re * z_Re; // A small speed optimization.
        var z_Im_squared = z_Im * z_Im; // A small speed optimization.
                      
        exponentialSmoothingSum += Math.exp( -(z_Re_squared + z_Im_squared) ); // Technically, this should be e^(-|z|). However, avoiding the expensive square root operation does not significantly effect the resulting image.              
        if (exponentialSmoothingSum >= 255) { // Don't cycle through the (gray) colors.
          exponentialSmoothingSum = 255;
        } // if

        if (z_Re_squared + z_Im_squared > 4) { // Checks if |z^2| is greater than 2. This approach avoids the expensive square root operation.
          c_belongsToMandelbrotSet = false; // This complex c value is not part of the Mandelbrot set (because it will always tend towards infinity under iteration).
          break; // Immediately check the next c value to see if it belongs to the Mandelbrot set or not.
        } // if
        
        // The next two lines perform Zn+1 = (Zn)^2 + c (recall that (x + yi)^2 = x^2 - y^2 + 2xyi, thus the real part is x^2 - y^2 and the imaginary part is 2xyi).
        z_Im = (2 * z_Re * z_Im) + c_Im; // We must calculate the next value of z_Im first because it depends on the current value of z_Re (not the next value of z_Re).
        z_Re = z_Re_squared - z_Im_squared + c_Re; // Calculate the next value of z_Re.
      } // for   
      
      if (c_belongsToMandelbrotSet) { // This complex c value is probably part of the Mandelbrot set because Zn did not tend toward infinity within MAX_ITERATIONS iterations.
        imageDataObjectData[currentPixel++] = 0; // Red. Note that there are 255 possible shades of red, green, blue, and alpha (i.e., opacity).
        imageDataObjectData[currentPixel++] = 0; // Green.
        imageDataObjectData[currentPixel++] = 0; // Blue.
        imageDataObjectData[currentPixel++] = 255; // Alpha (i.e., 0% transparency).
      } 
      else { // This complex c valus is definitely not part of the Mandelbrot set because Zn would tend toward infinity under iteration (i.e., |Zn| > 2).
        var pixelGrayscaleValue = 255 - exponentialSmoothingSum % 256; // Force the value of exponentialSmoothingSum to be between 0 and 255 inclusively. Note that all values for red, green, and blue are identical when using a grayscale.
        var adjustedPixelGrayscaleValue = pixelGrayscaleValue * grayscaleFactor;
        
        imageDataObjectData[currentPixel++] = adjustedPixelGrayscaleValue; // Because we mod by 256, the value of exponentialSmoothingSum will always be between 0 and 255.
        imageDataObjectData[currentPixel++] = adjustedPixelGrayscaleValue; // If exponentialSmoothingSum is 255 (it's maximum possible value), then 255 % 256 = 255.
        imageDataObjectData[currentPixel++] = adjustedPixelGrayscaleValue; // When exponentialSmoothingSum is 255, we have 255 - 255 = 0, so the shade values for RGB are all set to 0 (that is, the c-value pixel is rendered black - indicating that this particular c-value very slowly tends towards infinity).
        imageDataObjectData[currentPixel++] = 255; // Always draw the c-value pixels with no transparency.
        
        if (pixelGrayscaleValue > maxPixelGrayscaleValue) {
          maxPixelGrayscaleValue = pixelGrayscaleValue; // Determine the lightest shade of gray in case the user clicks the Lighten button.
        } // if
      } // if-else
    } // for
  } // for  
  
  self.postMessage({
    imageDataObject: imageDataObject,  
    maxPixelGrayscaleValue: maxPixelGrayscaleValue,
    workerID: evt.data.workerID,
    iterationSum: iterationSum
  });
} // self.onmessage

The worker thread code is contained within a single anonymous function:


self.onmessage = function(evt) { ... }

This anonymous function is invoked when a message is sent to it from the UI thread. The sent message is contained within evt.data. To improve performance, the data contained within the message is transferred to worker thread local variables:


var MAX_ITERATIONS = evt.data.MAX_ITERATIONS;
var ReMax = evt.data.ReMax;
var ReMin = evt.data.ReMin;
var ImMax = evt.data.ImMax;
var ImMin = evt.data.ImMin;
var grayscaleFactor = evt.data.grayscaleFactor;
var canvasWidth = evt.data.canvasWidth;
var canvasHeight = evt.data.canvasHeight;
var imageDataObject = evt.data.imageDataObject; // This is a copy of, not a reference to, globals.canvas.context.imageDataObject.

The Mandelbrot image calculation code is exactly as before except that instead of immediately drawing the image data array to the canvas, we pass it back to the calling UI thread (along with a few other items to be handled by the UI thread):


self.postMessage({
  imageDataObject: imageDataObject,  
  maxPixelGrayscaleValue: maxPixelGrayscaleValue,
  workerID: evt.data.workerID,
  iterationSum: iterationSum
});

This self.postMessage call invokes (and passes the object literal) to the following callback in the UI thread:


function workerCallback(evt) { // Receive the required data from the Web Worker to draw the Mandelbrot set to the canvas (plus a few other items).          
  if (fineDetailMandelbrotReceived) {
    return; // For some reason, the fine detail callback finished before the coarse detail callback. Don't display the coarse Mandelbrot image.
  }
  
  ctx.putImageData(evt.data.imageDataObject, 0, 0); // Render our carefully constructed canvas image data array to the canvas.
  globals.canvas.context.imageDataObject = evt.data.imageDataObject; 
  globals.maxPixelGrayscaleValue = evt.data.maxPixelGrayscaleValue; // Store this information in case the user clicks the Lighten button.          

  var elapsedMilliseconds = (new Date()) - startTime;
  elapsedTime.innerHTML = evt.data.workerID + ": " + evt.data.iterationSum.format() + " iterations in " + (elapsedMilliseconds / 1000).toFixed(2) + " seconds"; // Note that the UI element is not updated until after this block terminates (which is the desired behavior).            
  
  if (evt.data.workerID == "Fine detail") {
    fineDetailMandelbrotReceived = true;
    messageBox.innerHTML = DEFAULT_MESSAGE; // Erase the "Calculating..." message and replace it with the default message.
  } // if
} // workerCallback


That is, the workerCallback function is invoked by the worker thread when its task is complete. The object literal from the worker thread is contained in the associated event object (evt.data). The four pieces of information passed from the worker thread to the UI thread are:

  • evt.data.imageDataObject - this contains the completed Mandelbrot image in canvas data array form. ctx.putImageData(evt.data.imageDataObject, 0, 0) then draws the image to the canvas (in the UI thread).
  • evt.data.maxPixelGrayscaleValue - this contains the lightest shade of gray in the Mandelbrot image, which is generally needed if the user clicks the Lighten button.
  • workerID - this indicates from which worker thread the object literal came from. This is necessary to know if, in the off chance, the fine (high-detail) worker thread completed before the course (low-detail) worker thread:
    
    if (fineDetailMandelbrotReceived) {
      return; // For some reason, the fine detail callback finished before the coarse detail callback. Don't display the coarse Mandelbrot image.
    }
    
    
    
  • iterationSum - provides the number of iterations required to generate the requested Mandelbrot image. This value, along with the number of seconds necessary to calculate the Mandelbrot image (in the Fine detail worker thread), provides a performance metric for the Mandelbrot 8 application.

The availability of worker threads opens up many possible algorithms for improving performance. For example, instead of concurrently calculating a low-detail and high-detail image (in an attempt to avoiding a lengthy blank screen), two worker threads could be used to concurrently calculate the upper half and lower half of a high-detail Mandelbrot image. This approach, without discussion, is demonstrated in Mandelbrot 9 (right-click the page to view the source code) - the associated JavaScript files are mandelbrotWebWorkerManager.js and mandelbrotWebWorker.js.

In the next and final section, Mandelbrot Explorer, we improve the zoom box code so that a zoom box can be drawn starting from any corner.

Related topics

Mandelbrot Explorer

 

 

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