The Mandelbrot set was named after Benoit Mandelbrot, who first saw the shape at IBM’s Thomas J. Watson Research Centre on March 1st 1980. It’s place is in a field of mathematics called complex dynamics, having not looked at any mathematics for a good few years it took me some time to get my head round exactly what was going on, and I still only have an inkling of what it all means.
The image above – top left is arguably the most famous fractal; the three other shapes have been generated by zooming into the original fractal. The ‘image’ has infinite resolution, you can keep zooming in and it will always generate a new image. I’d say the only limitation is the browser / computer generating it.
One thing you will notice when zooming is the fact the Mandelbrot set is self-similar (or at least close to self-similar). At many points you will notice the original fractal shape, only on a smaller scale. This along with other repeating shapes creates a beautiful image purely generated by mathematics.
Note: Slight update to the render method here.
View a demo here. A few features I added:
- Add render loader and restyled the form layout
- User can switch between colour & grey-scale
- Ability to select a range of hues the render uses
- Possible to change the saturation and lightness of colours used
- Ability to rotate the canvas
- Change the width and height of the render area
- Select from a set of zoom / position presets
- A version using the Web Workers API in Firefox 3.5+ (See notes below on usage)
Note: As I mentioned above I have created a version using the Web Workers API found in Firefox 3.5+, but I strongly recommend using the standard version; I created it to see what difference it would make to the render time.