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mandelbrot2.htm
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mandelbrot2.htm
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<!DOCTYPE html>
<html>
<head>
<script>
var GRAPH1 = null;
var GRAPH2 = null;
function ComplexGraph(canvas, origin)
{
this.Color = "#0000ff";
this.Origin = origin;
this.Scale = 100.0; // Unit
this.Canvas = canvas;
this.Context = null;
this.R=1.0;
this.I=0.5;
this.Dragable = true;
this.Active = false;
this.Dragging = false;
}
ComplexGraph.prototype.RelativeMouseCoordinates = function (event) {
var totalOffsetX = 0;
var totalOffsetY = 0;
var canvasX = 0;
var canvasY = 0;
var currentElement = this.Canvas;
do{
totalOffsetX += currentElement.offsetLeft - currentElement.scrollLeft;
totalOffsetY += currentElement.offsetTop - currentElement.scrollTop;
}
while(currentElement = currentElement.offsetParent)
canvasX = event.pageX - totalOffsetX;
canvasY = event.pageY - totalOffsetY;
graphX = canvasX - this.Origin[0];
graphY = -(canvasY - this.Origin[1]);
return {x:graphX, y:graphY}
}
ComplexGraph.prototype.MouseMove = function(event) {
coords = this.RelativeMouseCoordinates(event);
if (this.Dragging) {
// Just move the tip to the mouse.
this.R = coords.x / this.Scale;
this.I = coords.y / this.Scale;
draw();
} else {
// Haw far is the event away from the tip (in pixels).
var tx = this.R*100.0;
var ty = this.I*100.0;
tx = tx - coords.x;
ty = ty - coords.y;
// Distance squared
dist = tx * tx + ty * ty;
if (dist <= 25.0 && ! this.Active) {
this.Active = true;
this.Draw(true);
}
if (dist > 25.0 && this.Active) {
this.Active = false;
this.Draw(true);
}
}
}
ComplexGraph.prototype.MouseDown = function() {
if (this.Active) {
this.Dragging = true;
}
}
ComplexGraph.prototype.MouseUp = function() {
this.Dragging = false;
}
ComplexGraph.prototype.Draw = function (vectorFlag) {
var c=this.Canvas;
var r = this.R;
var i = this.I;
var canvOK=1;
try {c.getContext("2d");}
catch (er) {canvOK=0;}
if (canvOK==1) {
this.Radius = Math.sqrt(r*r + i*i);
this.Theta = Math.atan2(i,r) * 180 / Math.PI;
if (this.Theta < 0.0) {
this.Theta += 360.0;
}
var ctx=c.getContext("2d");
//ctx.clearRect (this.Origin[0]-200 , this.Origin[1]-200, 400 , 410);
if (this.Dragable) {
var img=document.getElementById("mandelbrot");
ctx.drawImage(img,139,150);
}
// Draw the unit circle.
ctx.beginPath();
ctx.arc(this.Origin[0],this.Origin[1],100,0,2*Math.PI);
ctx.strokeStyle="#A0A0A0";
ctx.stroke();
ctx.closePath();
// Draw the Axes vector
ctx.beginPath();
ctx.moveTo(this.Origin[0]-180,this.Origin[1]);
ctx.lineTo(this.Origin[0]+180,this.Origin[1]);
ctx.strokeStyle="#000000";
ctx.stroke();
ctx.moveTo(this.Origin[0],this.Origin[1]-180);
ctx.lineTo(this.Origin[0],this.Origin[1]+180);
ctx.strokeStyle="#000000";
ctx.stroke();
ctx.closePath();
if (vectorFlag) {
this.DrawVectorTriangle([r,i], this.Color, [1,0], false);
}
// Draw the complex coordinates label
ctx.font="30px Arial";
var coordStr = "";
ctx.fillStyle=this.Color;
coordStr = coordStr + r.toFixed(2);
coordStr = coordStr + " + ";
coordStr = coordStr + i.toFixed(2) + "i";
ctx.fillText(coordStr, this.Origin[0]-195, this.Origin[1]-170);
// Draw the polar coordinates
var coordStr = "Angle: ";
coordStr = coordStr + this.Theta.toFixed(2);
coordStr = coordStr + ", Magnitude: ";
coordStr = coordStr + this.Radius.toFixed(2);
ctx.font="20px Arial";
ctx.fillStyle=this.Color;
ctx.fillText(coordStr, this.Origin[0]-195, this.Origin[1]+205);
// Pick a rainbow color for the count label
if (COUNT > 0) {
ctx.font="30px Arial";
var str = "";
str += COUNT;
ctx.beginPath();
ctx.font="50px Arial";
// Use the count to compute a cycling rainbow color.
var hue = (COUNT % 30) / 10.0;
// blue 0-1-2
var b = hue;
if (b > 1.0) { b = 2.0-b;}
if (b < 0.0) { b = 0.0;}
// Red 1-2-3
var r = hue - 1.0;
if (r > 1.0) { r = 2.0-r;}
if (r < 0.0) { r = 0.0;}
// green 2-3/0-1
var g = hue - 2.0;
if (g < -1.0) { g += 3.0; } // Wrap
if (g > 1.0) { g = 2.0-g;}
if (g < 0.0) { g = 0.0;}
// Softer curve for brighter colors.
r = Math.sin(r * Math.PI * 0.5) * 255;
b = Math.sin(b * Math.PI * 0.5) * 255;
g = Math.sin(g * Math.PI * 0.5) * 255;
// Now change this into a color.
color = "rgb("+Math.floor(r)+","+Math.floor(g)+","+Math.floor(b)+")";
ctx.fillStyle= color;
ctx.fillText(str, 840, 240);
ctx.closePath();
}
}
}
// For drawing the multiplcation composition.
// Base is for the multiplication demonstration.
// Transformation so [1,0] moves onto base.
// triFlag draws the base to tip line
ComplexGraph.prototype.DrawVectorTriangle = function (vect, color, base, triFlag) {
var ctx=this.Canvas.getContext("2d");
var thetaBase = Math.atan2(base[1], base[0]);
var thetaVect = Math.atan2(vect[1], vect[0]);
// Rotate the vector to match the base
var r = vect[0]*base[0] - vect[1]*base[1];
var i = vect[0]*base[1] + vect[1]*base[0];
// Draw the complex vector
ctx.beginPath();
ctx.moveTo(this.Origin[0], this.Origin[1]);
ctx.lineTo(this.Origin[0] + r*this.Scale, this.Origin[1] - i*this.Scale);
ctx.strokeStyle=color;
ctx.stroke();
ctx.closePath();
if (triFlag) {
// Close the triangle to (1,0) to better demonstrate muliptlication of magnitude.
// I would like to make this line dashed.
ctx.beginPath();
ctx.moveTo(this.Origin[0] + base[0]*this.Scale, this.Origin[1] - base[1]*this.Scale);
ctx.lineTo(this.Origin[0] + r*this.Scale, this.Origin[1] - i*this.Scale);
ctx.strokeStyle=color;
ctx.stroke();
ctx.closePath();
}
// Draw the arc
// Funky negatives because canvas y axis is flipped.
ctx.beginPath();
ctx.strokeStyle=color;
ctx.lineWidth = 5;
ctx.arc(this.Origin[0],this.Origin[1],10,-thetaVect-thetaBase, -thetaBase);
ctx.stroke();
ctx.closePath();
ctx.lineWidth = 1;
// Active end spot
var spotRadius = 3;
if (this.Dragable) {
var spotRadius = 6;
}
ctx.beginPath();
ctx.arc(this.Origin[0] + r*this.Scale, this.Origin[1] - i*this.Scale, spotRadius, 0, 2*Math.PI);
if (this.Dragable) {
ctx.lineWidth = 3;
ctx.strokeStyle="#FFFF00";
ctx.stroke();
ctx.lineWidth = 1;
}
ctx.closePath();
if (this.Active) {
ctx.fillStyle="#FFFF00";
} else {
ctx.fillStyle=this.Color;
}
ctx.fill();
}
var RUN = false;
var COUNT = 0;
var ITERATION = 0;
// Need these for the steps of the animation.
var Z = [0.0, 0.0];
var Z_SQUARED = [0.0, 0.0];
var Z_MAGNITUDE2 = 0.0;
function run() {
GRAPH2.R = GRAPH1.R;
GRAPH2.I = GRAPH1.I;
draw();
RADIUS = 0;
COUNT = 1;
RUN = true;
iterate1();
}
// Just draw Z.
function iterate1() {
if ( ! RUN) { return }
var ctx=GRAPH1.Canvas.getContext("2d");
ITERATION = 1;
Z = [GRAPH2.R, GRAPH2.I];
Z_MAGNITUDE2 = GRAPH2.R*GRAPH2.R + GRAPH2.I*GRAPH2.I;
var r = Z[0]*Z[0] - Z[1]*Z[1];
var i = Z[0]*Z[1] + Z[1]*Z[0];
Z_SQUARED = [r,i];
draw();
if (Z_MAGNITUDE2 > 4.0) {
RUN = false;
} else {
setTimeout(function(){iterate2()},1000);
}
}
// Animate the squaring of z.
function iterate2() {
ITERATION = 2;
draw();
setTimeout(function(){iterate3()},500);
}
// Animate the squaring of z.
function iterate3() {
GRAPH2.R = Z_SQUARED[0];
GRAPH2.I = Z_SQUARED[1];
ITERATION = 3;
draw();
setTimeout(function(){iterate4()},500);
}
// Animate the shift (addition of the constant).
function iterate4() {
var r = GRAPH2.R;
var i = GRAPH2.I;
// Add the constant C
GRAPH2.R += GRAPH1.R;
GRAPH2.I += GRAPH1.I;
ITERATION = 4;
draw();
++COUNT;
setTimeout(function(){iterate1()},1000);
}
function stop() {
RUN = false;
}
function mouseMove(event)
{
if (GRAPH1.Dragging) { RUN = false; }
if (GRAPH1) GRAPH1.MouseMove(event);
}
function mouseDown()
{
if (GRAPH1) GRAPH1.MouseDown();
}
function mouseUp()
{
if (GRAPH1) GRAPH1.MouseUp();
}
function draw()
{
var ctx=GRAPH1.Canvas.getContext("2d");
ctx.clearRect(0 , 0, 900 , 470);
// Draw titles on the graphs
ctx.beginPath();
ctx.font="30px Arial";
ctx.fillStyle=GRAPH1.Color;
ctx.fillText("C", GRAPH1.Origin[0]-10, GRAPH1.Origin[1]-225);
ctx.closePath();
// Highlight the part of the equation currently being graphed.
ctx.beginPath();
ctx.fillStyle=GRAPH2.Color;
ctx.fillText("=", GRAPH2.Origin[0]-65, GRAPH2.Origin[1]-225);
ctx.fillText("+", GRAPH2.Origin[0]+15, GRAPH2.Origin[1]-225);
ctx.closePath();
ctx.beginPath();
if (ITERATION == 1) {
ctx.fillStyle="#B00000";
} else {
ctx.fillStyle=GRAPH2.Color;
}
ctx.fillText("Z", GRAPH2.Origin[0]-90, GRAPH2.Origin[1]-225);
ctx.closePath();
ctx.beginPath();
if (ITERATION == 2 || ITERATION == 3) {
ctx.fillStyle="#B00000";
} else {
ctx.fillStyle=GRAPH2.Color;
}
ctx.fillText("Z*Z", GRAPH2.Origin[0]-40, GRAPH2.Origin[1]-225);
ctx.closePath();
ctx.beginPath();
if (ITERATION == 4) {
ctx.fillStyle="#B00000";
} else {
ctx.fillStyle=GRAPH2.Color;
}
ctx.fillText("C", GRAPH2.Origin[0] + 40, GRAPH2.Origin[1]-225);
ctx.closePath();
GRAPH1.Draw(true);
// Draw the termination circle.
ctx.beginPath();
if (Z_MAGNITUDE2 > 4) {
ctx.strokeStyle="#FF0000";
} else {
ctx.strokeStyle="#FFE0E0";
}
ctx.arc(GRAPH2.Origin[0],GRAPH2.Origin[1],200,0, 2.0*Math.PI);
ctx.stroke();
ctx.closePath();
// How we draw GRAPH2 depends on the iteration.
if (ITERATION <= 1) {
if (Z_MAGNITUDE2 > 4) {
GRAPH2.Color = "#FF0000";
} else {
GRAPH2.Color = "#00A000"
}
GRAPH2.Draw(true);
return;
}
GRAPH2.Draw(false);
GRAPH2.DrawVectorTriangle(Z, GRAPH2.Color, [1,0], true);
if (ITERATION > 2) {
GRAPH2.DrawVectorTriangle(Z, GRAPH2.Color, Z, true);
}
if (ITERATION > 3) {
ctx.beginPath();
r = Z_SQUARED[0];
i = Z_SQUARED[1];
ctx.moveTo(GRAPH2.Origin[0] + r*GRAPH2.Scale, GRAPH2.Origin[1] - i*GRAPH2.Scale);
r = GRAPH2.R;
i = GRAPH2.I;
ctx.lineTo(GRAPH2.Origin[0] + r*GRAPH2.Scale, GRAPH2.Origin[1] - i*GRAPH2.Scale);
ctx.strokeStyle=GRAPH1.Color;
ctx.stroke();
ctx.closePath();
}
}
function main()
{
var canvas = document.getElementById("myCanvas")
var canvOK=1;
try {canvas.getContext("2d");}
catch (er) {
alert("Could not initialize canvas");
return;
}
var ctx=canvas.getContext("2d");
GRAPH1=new ComplexGraph(canvas, [300, 250]);
GRAPH1.Color = "#0000FF"
GRAPH2=new ComplexGraph(canvas, [700, 250]);
GRAPH2.Color = "#00A000"
GRAPH2.R = 0.0;
GRAPH2.I = 0.0;
GRAPH2.Dragable = false;
draw();
}
</script>
<body onload="main()">
<img id="mandelbrot" src="mandelbrot3.jpg" width="254" height="200" hidden="true">
<canvas id="myCanvas" width="900" height="470" style="border:1px solid #d3d3d3;"
onmousemove="mouseMove(event)"
onmousedown="mouseDown()"
onmouseup="mouseUp()"
>
Your browser does not support the HTML5 canvas tag.</canvas>
</br>
<button type="button" onclick="run()">Go!</button>
<button type="button" onclick="stop()">Stop</button>
</br>
We use simple complex arithmatic to create a chaotic sequence and fractal function.
</br>
Next: Videos
</br>
<a href="http://www.youtube.com/watch?v=RYVmd7H7gzw">Fast Zoom Video</a>
</br>
<a href="http://www.youtube.com/watch?v=9G6uO7ZHtK8">Slow Zoom Video</a>
</br>
<a href="http://www.youtube.com/watch?v=VSDI84Mm-hI">Scale of the Universe</a>
</body>
</html>