## Fun with fractals using HTML5

I was writing some fractal code and thought that it would be interesting to see if it could be done in Javascript with graphical output provided by the HTML5 <canvas> element. As you can see, it worked just fine, albeit a little bit slow.

<html> <head> <script src="fractal.js" type="text/javascript" language="javascript"></script> </head> <body onload="drawFractal();"> <canvas style="border: 1px solid black" id="canvas" width="500" height="500"></canvas> </body> </html>

// file: fractal.js // draw a point on our canvas element using the rect function // set to draw a 1x1 square function drawPoint( in_x, in_y ) { var canvas = document.getElementById( "canvas" ); var ctx = canvas.getContext( "2d" ); ctx.fillStyle = "rgb(0,0,0)"; ctx.fillRect( in_x, in_y, 1, 1 ); } // data structure that represents a complex number ( re + im ) function Complex( in_re, in_im ) { this.re = in_re; this.im = in_im; } // multiplication function for 2 complex numbers.. Performs FOIL function ComplexMult( in_c1, in_c2 ) { var real = ( in_c1.re * in_c2.re ) - ( in_c1.im * in_c2.im ); var imag = ( in_c1.re * in_c2.im ) + ( in_c1.im * in_c2.re ); return new Complex( real, imag ); } // addition of two complex numbers function ComplexAdd( in_c1, in_c2 ) { return new Complex( in_c1.re + in_c2.re, in_c1.im + in_c2.im ); } // absolute value of a complex number using sqrt( a^2 + b^2 ) form function ComplexAbs( in_c ) { return Math.sqrt( in_c.re*in_c.re + in_c.im*in_c.im ); } function drawFractal() { // resolution of our pixel image var x = 500; var y = 500; // real axis max/min var remin = -2; var remax = 2; // imaginary axis max/min var immin = -2; var immax = 2; // calculate the ranges from the bounds var rerange = remax - remin; var imrange = immax - immin; // number of iterations that we peform on each pixel var depth = 25; // iterate over each pixel in our output image for( var i=0; i < x; i++ ) { for( var j=0; j < y; j++ ) { var zn = new Complex( 0, 0 ); // we need a mapping from pixels to complex plane var re = ( rerange/x ) * i - rerange/2; var im = ( imrange/y ) * j - imrange/2; var c = new Complex( re, im ); // solve the iterative function for n = depth for( var n=1; n <= depth; n++ ) { // equation is zn = zn*zn + c zn = ComplexAdd( ComplexMult( zn, zn ), c ); } // test to see if the point is in the set using 2 as the // boundary if( ComplexAbs( zn ) < 2 ) { drawPoint( i, j ); } } } }

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I had a similar idea, JavaScript plus is a powerful combination. Nice to see! But I agree that it seems a little slow.

Fredrik KJanuary 2, 2010 at 10:55 am

..plus the canvas-element..

Fredrik KJanuary 2, 2010 at 10:57 am

I wrote an interactive fractal renderer. Lets you drag out a zoom window with the mouse and increase the number of iterations by clicking a button.

My Mandelbrot set starts at 100 iterations. Opera seems to by, by far, the fastest browser for my code.

http://dougx.net/fractals/fractals.html

DougXAugust 7, 2010 at 9:50 am