Bee Eee Blog » fractals http://blog.bee-eee.com -- C# hints and tips Wed, 23 Dec 2009 19:00:47 +0000 en hourly 1 http://wordpress.org/?v=3.0.1 c# Mandelbrot fractal unleashed! http://blog.bee-eee.com/2008/05/15/c-mandelbrot-fractal-unleashed/ http://blog.bee-eee.com/2008/05/15/c-mandelbrot-fractal-unleashed/#comments Fri, 16 May 2008 03:17:28 +0000 brian http://blog.bee-eee.com/2008/05/15/c-mandelbrot-fractal-unleashed/ I remember the first time I saw the Mandelbrot set.  It was incredible!  After I had successfully programmed at it on my 8088 (a very old DOS computer).  I would wait 10 minutes at a time for a screen to pop up.  The detail was nothing short of amazing.  The swirls, the shapes, the colors.  The neatest thing was the ability to zoom into it to reveal more and more and more detail.

Well it’s been many years and computers have improved a great deal as have the tools to program them.  So I wrote another Mandelbrot explorer.

Mandelbrot Image

What is the Mandelbrot set? Well….  In short it is Xn+1 = Xn2 + C iterated until the magnitude of Xn is greater than 4 or the maximum number of iterations is met then the number of iterations is used as the color of the pixel.  Xn is a complex number, C is another complex number where the x coordinate of the pixel defines the real part and the y coordinate defines the imaginary part of the number. The magnitude is defined as X2 + Absolute Value of (Xi2).  Then this process is repeated for each pixel.  Holy smoke that is a mouthful!

Anyway take a peek at the code if you’d like and surely get the app and have fun exploring the Mandelbrot set.

To zoom in a spot just click on it.  The number is the number of iterations.  The more iterations the deeper the pattern goes (well until you run into percision problems).

Mandelbrot Executable

Mandelbrot source code.

Have fun!

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