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Here's my JSFiddle http://jsfiddle.net/kgEuM/

Here's my JSFiddle http://jsfiddle.net/Kuligoawesome/3VsCu/

// Global variables
const FPS = 100;// FrameRate
var canvas = null;
var ctx = null;
window.onload = Init;

var bInstantDraw = true;
var MOVES_PER_UPDATE = 1000; //How many pixels get placed down
var bDone = false;
var width; //canvas width
var height; //canvas height
var colorSteps = 32;

var imageData;
var grid;
var colors;

var currentPos;
var prevPositions;

// This is called when the page loads
function Init()
{
    canvas = document.getElementById(   'canvas'); // Get the HTML element with the ID of 'canvas'
    width = canvas.width;
    height = canvas.height;
    ctx = canvas.getContext('2d'); // This is necessary, but I don't know exactly what it does
    
    imageData = ctx.createImageData(width,height); //Needed to do pixel manipulation
    
    grid = []; //Grid for the labyrinth algorithm
    colors = []; //Array of all colors
    prevPositions = []; //Array of previous positions, used for the recursive backtracker algorithm
    
    for(var x = 0; x < width; x++)
    {
        grid.push(new Array());
        for(var y = 0; y < height; y++)
        {
            grid[x].push(0); //Set up the grid
        }
    }
    
    for(var r = 0; r < colorSteps; r++)
    {
        for(var g = 0; g < colorSteps; g++)
        {
            for(var b = 0; b < colorSteps; b++)
            {
                colors.push(new Color(r * Math.ceil(255 / (colorSteps - 1)), g * Math.ceil(255 / (colorSteps - 1)), b * Math.ceil(255 / (colorSteps - 1))));
                //Fill the array with all colors
            }
        }
    }
    
    colors.sort(function(a,b)
    {
        if (a.r < b.r)
            return -1;
        if (a.r > b.r)
            return 1;
        if (a.g < b.g)
            return 1;
        if (a.g > b.g)
            return -1;
        if (a.b < b.b)
            return -1;
        if (a.b > b.b)
            return 1;
        
        
        return 0;
    });
    
    currentPos = new Point(Math.floor(Math.random() * width),Math.floor(Math.random() * height)); 
    
    grid[currentPos.x][currentPos.y] = 1;
    prevPositions.push(currentPos);
    ChangePixel(imageData, currentPos.x, currentPos.y, colors.pop());
    
    if(bInstantDraw)
    {
        do
        {
            var notMoved = true;
            while(notMoved)
            {
                var availableSpaces = CheckForSpaces(grid);
                
                if(availableSpaces.length > 0)
                {
                    var test = availableSpaces[Math.floor(Math.random() * availableSpaces.length)];
                    prevPositions.push(currentPos);
                    currentPos = test;
                    grid[currentPos.x][currentPos.y] = 1;
                    ChangePixel(imageData, currentPos.x, currentPos.y, colors.pop());
                    notMoved = false;
                }
                else
                {
                    if(prevPositions.length != 0)
                    {
                        currentPos = prevPositions.pop();
                    }
                    else
                    {
                        break;
                    }
                }
            }
        }
        while(prevPositions.length > 0)
        
        ctx.putImageData(imageData,0,0);
        //document.write('<img src="'+canvas.toDataURL("image/png")+'"/>');
    }
    else
    {
        setInterval(GameLoop, 1000 / FPS);
    }
}

// Main program loop
function GameLoop()
{
    Update();
    Draw();
}

// Game logic goes here
function Update()
{
    if(!bDone)
    {
        var counter = MOVES_PER_UPDATE;
        while(counter > 0) //For speeding up the drawing
        {
            var notMoved = true;
            while(notMoved)
            {
                var availableSpaces = CheckForSpaces(grid); //Find available spaces
                
                if(availableSpaces.length > 0) //If there are available spaces
                {
                    prevPositions.push(currentPos); //add old position to prevPosition array
                    currentPos = availableSpaces[Math.floor(Math.random() * availableSpaces.length)]; //pick a random available space
                    grid[currentPos.x][currentPos.y] = 1; //set that space to filled
                    ChangePixel(imageData, currentPos.x, currentPos.y, colors.pop()); //pop color of the array and put it in that space
                    notMoved = false;
                }
                else
                {
                    if(prevPositions.length != 0)
                    {
                        currentPos = prevPositions.pop(); //pop to previous position where spaces are available
                    }
                    else
                    {
                        ctx.putImageData(imageData,0,0);
                        bDone = true;
                        break;
                    }
                }
            }
            counter--;
        }
    }
}
function Draw()
{
    // Clear the screen
    ctx.clearRect(0, 0, ctx.canvas.width, ctx.canvas.height);
    ctx.fillStyle='#000000';
    ctx.fillRect(0, 0, ctx.canvas.width, ctx.canvas.height);
    
    ctx.putImageData(imageData,0,0);
}

function CheckForSpaces(inGrid) //Checks for available spaces then returns back all available spaces
{
    var availableSpaces = [];
    
    if(currentPos.x > 0 && inGrid[currentPos.x - 1][currentPos.y] == 0)
    {
        availableSpaces.push(new Point(currentPos.x - 1, currentPos.y));
    }
    
    if(currentPos.x < width - 1 && inGrid[currentPos.x + 1][currentPos.y] == 0)
    {
        availableSpaces.push(new Point(currentPos.x + 1, currentPos.y));
    }
    
    if(currentPos.y > 0 && inGrid[currentPos.x][currentPos.y - 1] == 0)
    {
        availableSpaces.push(new Point(currentPos.x, currentPos.y - 1));
    }
    
    if(currentPos.y < height - 1 && inGrid[currentPos.x][currentPos.y + 1] == 0)
    {
        availableSpaces.push(new Point(currentPos.x, currentPos.y + 1));
    }
    
    return availableSpaces;
}

function ChangePixel(data, x, y, color) //Quick function to simplify changing pixels
{
    data.data[((x + (y * width)) * 4) + 0] = color.r;
    data.data[((x + (y * width)) * 4) + 1] = color.g;
    data.data[((x + (y * width)) * 4) + 2] = color.b;
    data.data[((x + (y * width)) * 4) + 3] = 255;
}

256x128 picture, colors sorted red->green->blue

256x128 picture, colors sorted blue->green->red

256x128 picture, colors sorted hue->luminance->saturation

And finally a GIF of one being generated

Here's my JSFiddle http://jsfiddle.net/kgEuM/

// Global variables
const FPS = 60;// FrameRate
var canvas = null;
var ctx = null;

var bInstantDraw = false;
var MOVES_PER_UPDATE = 50; //How many pixels get placed down
var bDone = false;
var width; //canvas width
var height; //canvas height
var colorSteps = 32;

var imageData;
var grid;
var colors;

var currentPos;
var prevPositions;

// This is called when the page loads
function Init()
{
    canvas = document.getElementById('canvas'); // Get the HTML element with the ID of 'canvas'
    width = canvas.width;
    height = canvas.height;
    ctx = canvas.getContext('2d'); // This is necessary, but I don't know exactly what it does
    
    imageData = ctx.createImageData(width,height); //Needed to do pixel manipulation
    
    grid = []; //Grid for the labyrinth algorithm
    colors = []; //Array of all colors
    prevPositions = []; //Array of previous positions, used for the recursive backtracker algorithm
    
    for(var r = 0; r < colorSteps; r++)
    {
        for(var g = 0; g < colorSteps; g++)
        {
            for(var b = 0; b < colorSteps; b++)
            {
                colors.push(new Color(r * 255 / (colorSteps - 1), g * 255 / (colorSteps - 1), b * 255 / (colorSteps - 1)));
                //Fill the array with all colors
            }
        }
    }
    
    colors.sort(function(a,b)
    {
        if (a.r < b.r)
            return -1;
        if (a.r > b.r)
            return 1;
        if (a.g < b.g)
            return -1;
        if (a.g > b.g)
            return 1;
        if (a.b < b.b)
            return -1;
        if (a.b > b.b)
            return 1;
        return 0;
    });
    
    for(var x = 0; x < width; x++)
    {
        grid.push(new Array());
        for(var y = 0; y < height; y++)
        {
            grid[x].push(0); //Set up the grid
            //ChangePixel(imageData, x, y, colors[x + (y * width)]);
        }
    }
    
    currentPos = new Point(Math.floor(Math.random() * width),Math.floor(Math.random() * height)); 
    
    grid[currentPos.x][currentPos.y] = 1;
    prevPositions.push(currentPos);
    ChangePixel(imageData, currentPos.x, currentPos.y, colors.pop());
    
    if(bInstantDraw)
    {
        do
        {
            var notMoved = true;
            while(notMoved)
            {
                var availableSpaces = CheckForSpaces(grid);
                
                if(availableSpaces.length > 0)
                {
                    var test = availableSpaces[Math.floor(Math.random() * availableSpaces.length)];
                    prevPositions.push(currentPos);
                    currentPos = test;
                    grid[currentPos.x][currentPos.y] = 1;
                    ChangePixel(imageData, currentPos.x, currentPos.y, colors.pop());
                    notMoved = false;
                }
                else
                {
                    if(prevPositions.length != 0)
                    {
                        currentPos = prevPositions.pop();
                    }
                    else
                    {
                        break;
                    }
                }
            }
        }
        while(prevPositions.length > 0)
        
        ctx.putImageData(imageData,0,0);
    }
    else
    {
        setInterval(GameLoop, 1000 / FPS);
    }
}

// Main program loop
function GameLoop()
{
    Update();
    Draw();
}

// Game logic goes here
function Update()
{
    if(!bDone)
    {
        var counter = MOVES_PER_UPDATE;
        while(counter > 0) //For speeding up the drawing
        {
            var notMoved = true;
            while(notMoved)
            {
                var availableSpaces = CheckForSpaces(grid); //Find available spaces
                
                if(availableSpaces.length > 0) //If there are available spaces
                {
                    prevPositions.push(currentPos); //add old position to prevPosition array
                    currentPos = availableSpaces[Math.floor(Math.random() * availableSpaces.length)]; //pick a random available space
                    grid[currentPos.x][currentPos.y] = 1; //set that space to filled
                    ChangePixel(imageData, currentPos.x, currentPos.y, colors.pop()); //pop color of the array and put it in that space
                    notMoved = false;
                }
                else
                {
                    if(prevPositions.length != 0)
                    {
                        currentPos = prevPositions.pop(); //pop to previous position where spaces are available
                    }
                    else
                    {
                        bDone = true;
                        break;
                    }
                }
            }
            counter--;
        }
    }
}
function Draw()
{
    // Clear the screen
    ctx.clearRect(0, 0, ctx.canvas.width, ctx.canvas.height);
    ctx.fillStyle='#000000';
    ctx.fillRect(0, 0, ctx.canvas.width, ctx.canvas.height);
    
    ctx.putImageData(imageData,0,0);
}

function CheckForSpaces(inGrid) //Checks for available spaces then returns back all available spaces
{
    var availableSpaces = [];
    
    if(currentPos.x > 0 && inGrid[currentPos.x - 1][currentPos.y] == 0)
    {
        availableSpaces.push(new Point(currentPos.x - 1, currentPos.y));
    }
    
    if(currentPos.x < width - 1 && inGrid[currentPos.x + 1][currentPos.y] == 0)
    {
        availableSpaces.push(new Point(currentPos.x + 1, currentPos.y));
    }
    
    if(currentPos.y > 0 && inGrid[currentPos.x][currentPos.y - 1] == 0)
    {
        availableSpaces.push(new Point(currentPos.x, currentPos.y - 1));
    }
    
    if(currentPos.y < height - 1 && inGrid[currentPos.x][currentPos.y + 1] == 0)
    {
        availableSpaces.push(new Point(currentPos.x, currentPos.y + 1));
    }
    
    return availableSpaces;
}

function ChangePixel(data, x, y, color) //Quick function to simplify changing pixels
{
    data.data[((x + (y * width)) * 4) + 0] = color.r;
    data.data[((x + (y * width)) * 4) + 1] = color.g;
    data.data[((x + (y * width)) * 4) + 2] = color.b;
    data.data[((x + (y * width)) * 4) + 3] = 255;
}

/*Needed Classes*/
function Point(xIn, yIn)
{
    this.x = xIn;
    this.y = yIn;
}

function Color(r, g, b)
{
    this.r = r;
    this.g = g;
    this.b = b;
    this.hue = Math.atan2(Math.sqrt(3) * (this.g - this.b), 2 * this.r - this.g, this.b);
    this.min = Math.min(this.r, this.g);
    this.min = Math.min(this.min, this.b);
    this.min /= 255;
    this.max = Math.max(this.r, this.g);
    this.max = Math.max(this.max, this.b);
    this.max /= 255;
    this.luminance = (this.min + this.max) / 2;
    if(this.min === this.max)
    {
        this.saturation = 0;
    }
    else if(this.luminance < 0.5)
    {
        this.saturation = (this.max - this.min) / (this.max + this.min);
    }
    else if(this.luminance >= 0.5)
    {
        this.saturation = (this.max - this.min) / (2 - this.max - this.min);
    }
}

256x128 picture, colors sorted red->green->blue

256x128 picture, colors sorted blue->green->red

256x128 picture, colors sorted hue->luminance->saturation

And finally a GIF of one being generated

// Global variables
const FPS = 100;// FrameRate
var canvas = null;
var ctx = null;
window.onload = Init;

var bInstantDraw = true;
var MOVES_PER_UPDATE = 1000; //How many pixels get placed down
var bDone = false;
var width; //canvas width
var height; //canvas height
var colorSteps = 32;

var imageData;
var grid;
var colors;

var currentPos;
var prevPositions;

// This is called when the page loads
function Init()
{
    canvas = document.getElementById(   'canvas'); // Get the HTML element with the ID of 'canvas'
    width = canvas.width;
    height = canvas.height;
    ctx = canvas.getContext('2d'); // This is necessary, but I don't know exactly what it does
    
    imageData = ctx.createImageData(width,height); //Needed to do pixel manipulation
    
    grid = []; //Grid for the labyrinth algorithm
    colors = []; //Array of all colors
    prevPositions = []; //Array of previous positions, used for the recursive backtracker algorithm
    
    for(var x = 0; x < width; x++)
    {
        grid.push(new Array());
        for(var y = 0; y < height; y++)
        {
            grid[x].push(0); //Set up the grid
        }
    }
    
    for(var r = 0; r < colorSteps; r++)
    {
        for(var g = 0; g < colorSteps; g++)
        {
            for(var b = 0; b < colorSteps; b++)
            {
                colors.push(new Color(r * Math.ceil(255 / (colorSteps - 1)), g * Math.ceil(255 / (colorSteps - 1)), b * Math.ceil(255 / (colorSteps - 1))));
                //Fill the array with all colors
            }
        }
    }
    
    colors.sort(function(a,b)
    {
        if (a.r < b.r)
            return -1;
        if (a.r > b.r)
            return 1;
        if (a.g < b.g)
            return 1;
        if (a.g > b.g)
            return -1;
        if (a.b < b.b)
            return -1;
        if (a.b > b.b)
            return 1;
        
        
        return 0;
    });
    
    currentPos = new Point(Math.floor(Math.random() * width),Math.floor(Math.random() * height)); 
    
    grid[currentPos.x][currentPos.y] = 1;
    prevPositions.push(currentPos);
    ChangePixel(imageData, currentPos.x, currentPos.y, colors.pop());
    
    if(bInstantDraw)
    {
        do
        {
            var notMoved = true;
            while(notMoved)
            {
                var availableSpaces = CheckForSpaces(grid);
                
                if(availableSpaces.length > 0)
                {
                    var test = availableSpaces[Math.floor(Math.random() * availableSpaces.length)];
                    prevPositions.push(currentPos);
                    currentPos = test;
                    grid[currentPos.x][currentPos.y] = 1;
                    ChangePixel(imageData, currentPos.x, currentPos.y, colors.pop());
                    notMoved = false;
                }
                else
                {
                    if(prevPositions.length != 0)
                    {
                        currentPos = prevPositions.pop();
                    }
                    else
                    {
                        break;
                    }
                }
            }
        }
        while(prevPositions.length > 0)
        
        ctx.putImageData(imageData,0,0);
        document.write('<img src="'+canvas.toDataURL("image/png")+'"/>');
    }
    else
    {
        setInterval(GameLoop, 1000 / FPS);
    }
}

// Main program loop
function GameLoop()
{
    Update();
    Draw();
}

// Game logic goes here
function Update()
{
    if(!bDone)
    {
        var counter = MOVES_PER_UPDATE;
        while(counter > 0) //For speeding up the drawing
        {
            var notMoved = true;
            while(notMoved)
            {
                var availableSpaces = CheckForSpaces(grid); //Find available spaces
                
                if(availableSpaces.length > 0) //If there are available spaces
                {
                    prevPositions.push(currentPos); //add old position to prevPosition array
                    currentPos = availableSpaces[Math.floor(Math.random() * availableSpaces.length)]; //pick a random available space
                    grid[currentPos.x][currentPos.y] = 1; //set that space to filled
                    ChangePixel(imageData, currentPos.x, currentPos.y, colors.pop()); //pop color of the array and put it in that space
                    notMoved = false;
                }
                else
                {
                    if(prevPositions.length != 0)
                    {
                        currentPos = prevPositions.pop(); //pop to previous position where spaces are available
                    }
                    else
                    {
                        ctx.putImageData(imageData,0,0);
                        bDone = true;
                        break;
                    }
                }
            }
            counter--;
        }
    }
}
function Draw()
{
    // Clear the screen
    ctx.clearRect(0, 0, ctx.canvas.width, ctx.canvas.height);
    ctx.fillStyle='#000000';
    ctx.fillRect(0, 0, ctx.canvas.width, ctx.canvas.height);
    
    ctx.putImageData(imageData,0,0);
}

function CheckForSpaces(inGrid) //Checks for available spaces then returns back all available spaces
{
    var availableSpaces = [];
    
    if(currentPos.x > 0 && inGrid[currentPos.x - 1][currentPos.y] == 0)
    {
        availableSpaces.push(new Point(currentPos.x - 1, currentPos.y));
    }
    
    if(currentPos.x < width - 1 && inGrid[currentPos.x + 1][currentPos.y] == 0)
    {
        availableSpaces.push(new Point(currentPos.x + 1, currentPos.y));
    }
    
    if(currentPos.y > 0 && inGrid[currentPos.x][currentPos.y - 1] == 0)
    {
        availableSpaces.push(new Point(currentPos.x, currentPos.y - 1));
    }
    
    if(currentPos.y < height - 1 && inGrid[currentPos.x][currentPos.y + 1] == 0)
    {
        availableSpaces.push(new Point(currentPos.x, currentPos.y + 1));
    }
    
    return availableSpaces;
}

function ChangePixel(data, x, y, color) //Quick function to simplify changing pixels
{
    data.data[((x + (y * width)) * 4) + 0] = color.r;
    data.data[((x + (y * width)) * 4) + 1] = color.g;
    data.data[((x + (y * width)) * 4) + 2] = color.b;
    data.data[((x + (y * width)) * 4) + 3] = 255;
}

// Global variables
const FPS = 100;// FrameRate
var canvas = null;
var ctx = null;
window.onload = Init;

var bInstantDraw = true;
var MOVES_PER_UPDATE = 1000; //How many pixels get placed down
var bDone = false;
var width; //canvas width
var height; //canvas height
var colorSteps = 32;

var imageData;
var grid;
var colors;

var currentPos;
var prevPositions;

// This is called when the page loads
function Init()
{
    canvas = document.getElementById(   'canvas'); // Get the HTML element with the ID of 'canvas'
    width = canvas.width;
    height = canvas.height;
    ctx = canvas.getContext('2d'); // This is necessary, but I don't know exactly what it does
    
    imageData = ctx.createImageData(width,height); //Needed to do pixel manipulation
    
    grid = []; //Grid for the labyrinth algorithm
    colors = []; //Array of all colors
    prevPositions = []; //Array of previous positions, used for the recursive backtracker algorithm
    
    for(var x = 0; x < width; x++)
    {
        grid.push(new Array());
        for(var y = 0; y < height; y++)
        {
            grid[x].push(0); //Set up the grid
        }
    }
    
    for(var r = 0; r < colorSteps; r++)
    {
        for(var g = 0; g < colorSteps; g++)
        {
            for(var b = 0; b < colorSteps; b++)
            {
                colors.push(new Color(r * Math.ceil(255 / (colorSteps - 1)), g * Math.ceil(255 / (colorSteps - 1)), b * Math.ceil(255 / (colorSteps - 1))));
                //Fill the array with all colors
            }
        }
    }
    
    colors.sort(function(a,b)
    {
        if (a.r < b.r)
            return -1;
        if (a.r > b.r)
            return 1;
        if (a.g < b.g)
            return 1;
        if (a.g > b.g)
            return -1;
        if (a.b < b.b)
            return -1;
        if (a.b > b.b)
            return 1;
        
        
        return 0;
    });
    
    currentPos = new Point(Math.floor(Math.random() * width),Math.floor(Math.random() * height)); 
    
    grid[currentPos.x][currentPos.y] = 1;
    prevPositions.push(currentPos);
    ChangePixel(imageData, currentPos.x, currentPos.y, colors.pop());
    
    if(bInstantDraw)
    {
        do
        {
            var notMoved = true;
            while(notMoved)
            {
                var availableSpaces = CheckForSpaces(grid);
                
                if(availableSpaces.length > 0)
                {
                    var test = availableSpaces[Math.floor(Math.random() * availableSpaces.length)];
                    prevPositions.push(currentPos);
                    currentPos = test;
                    grid[currentPos.x][currentPos.y] = 1;
                    ChangePixel(imageData, currentPos.x, currentPos.y, colors.pop());
                    notMoved = false;
                }
                else
                {
                    if(prevPositions.length != 0)
                    {
                        currentPos = prevPositions.pop();
                    }
                    else
                    {
                        break;
                    }
                }
            }
        }
        while(prevPositions.length > 0)
        
        ctx.putImageData(imageData,0,0);
        //document.write('<img src="'+canvas.toDataURL("image/png")+'"/>');
    }
    else
    {
        setInterval(GameLoop, 1000 / FPS);
    }
}

// Main program loop
function GameLoop()
{
    Update();
    Draw();
}

// Game logic goes here
function Update()
{
    if(!bDone)
    {
        var counter = MOVES_PER_UPDATE;
        while(counter > 0) //For speeding up the drawing
        {
            var notMoved = true;
            while(notMoved)
            {
                var availableSpaces = CheckForSpaces(grid); //Find available spaces
                
                if(availableSpaces.length > 0) //If there are available spaces
                {
                    prevPositions.push(currentPos); //add old position to prevPosition array
                    currentPos = availableSpaces[Math.floor(Math.random() * availableSpaces.length)]; //pick a random available space
                    grid[currentPos.x][currentPos.y] = 1; //set that space to filled
                    ChangePixel(imageData, currentPos.x, currentPos.y, colors.pop()); //pop color of the array and put it in that space
                    notMoved = false;
                }
                else
                {
                    if(prevPositions.length != 0)
                    {
                        currentPos = prevPositions.pop(); //pop to previous position where spaces are available
                    }
                    else
                    {
                        ctx.putImageData(imageData,0,0);
                        bDone = true;
                        break;
                    }
                }
            }
            counter--;
        }
    }
}
function Draw()
{
    // Clear the screen
    ctx.clearRect(0, 0, ctx.canvas.width, ctx.canvas.height);
    ctx.fillStyle='#000000';
    ctx.fillRect(0, 0, ctx.canvas.width, ctx.canvas.height);
    
    ctx.putImageData(imageData,0,0);
}

function CheckForSpaces(inGrid) //Checks for available spaces then returns back all available spaces
{
    var availableSpaces = [];
    
    if(currentPos.x > 0 && inGrid[currentPos.x - 1][currentPos.y] == 0)
    {
        availableSpaces.push(new Point(currentPos.x - 1, currentPos.y));
    }
    
    if(currentPos.x < width - 1 && inGrid[currentPos.x + 1][currentPos.y] == 0)
    {
        availableSpaces.push(new Point(currentPos.x + 1, currentPos.y));
    }
    
    if(currentPos.y > 0 && inGrid[currentPos.x][currentPos.y - 1] == 0)
    {
        availableSpaces.push(new Point(currentPos.x, currentPos.y - 1));
    }
    
    if(currentPos.y < height - 1 && inGrid[currentPos.x][currentPos.y + 1] == 0)
    {
        availableSpaces.push(new Point(currentPos.x, currentPos.y + 1));
    }
    
    return availableSpaces;
}

function ChangePixel(data, x, y, color) //Quick function to simplify changing pixels
{
    data.data[((x + (y * width)) * 4) + 0] = color.r;
    data.data[((x + (y * width)) * 4) + 1] = color.g;
    data.data[((x + (y * width)) * 4) + 2] = color.b;
    data.data[((x + (y * width)) * 4) + 3] = 255;
}