FractalJB can be used to view the Mandelbrot Set fractal. There have been many applications written for viewing the Mandelbrot Set, but I have not found one which has all the features I wanted.

A video demonstrating FractalJB:

Gallery - A collection of images created using FractalJB. Any of these images can be dragged from a browser into the FractalJB window, for further exploration, provided you browser supports drag and drop (Tested on Firefox and Google).

1. The option of drawing the pure Mandelbrot Set with no iteration bands.

2. Save all the settings which generate an image of the set as metadata embedded within a PNG image file.

3. Extract and apply the settings embedded as metadata within a PNG image file created by FractalJB.

4. Zoom by selection box ensuring precise composition of an image.

5. Complete control over iteration band colouring.

6. Facility to resize and reposition a zoom selection box before zooming.

7. Complete control over the number of samples per pixel to reduce aliasing of the image. I do not know of any other applications which allow more than 4 samples per pixel.

8. Drag and drop capability from desktop, file managers and web browsers.

9. Feedback on the progress of rendering an image.

10. Show orbits of a point in real time.

11. Blur anti aliasing.

12. Image rotation.

I do not know of any other applications (including proprietary) which have all the above features. For example even the mature and efficient Fractal eXtreme application lacks all but features 10, 12.

Linux, Windows, Mac, Solaris. Java must be installed.

The Mandelbrot Set is the set of numbers *c* ϵ ℂ where the sequence *zₙ*₊₁ = *zₙ*² + *c* starting at *z*₀ = 0 is bounded.

The symbol ℂ represents the set of all complex numbers. Complex numbers can be represented geometrically as points on the complex plane, which is related to the the Cartesian plane. A coordinate (*a*, *b*) is positioned on the Cartesian plane by moving a distance *a* along the positive *x*-axis away from the origin, and then moving a distance of *b* in the direction of the positive *y*-axis. On the Complex plane the *x*-axis becomes the real axis and the *y*-axis becomes the imaginary axis. The number *a* + *bi* is positioned in the same location as the coordinate (*a*, *b*).

The diagram below shows the Mandelbrot set in the complex plane as the black area.

Detailed explanation - This is my attempt to explain the Mandelbrot set assuming only basic algebra and arithmetic knowledge.

The Amazing Mandelbrot Set Tutorial - This is a 15 minute YouTube video explaining what the Mandelbrot set is and how it is plotted by a computer.

The Colours of Infinity - This is a TV documentary made in 1995, presented by Arthur C.Clarke. It's not technical, but explores the discovery and significance of the Mandelbrot Set and fractals generally. There are interviews with Professor Benoît Mandelbrot, Professor Ian Stewart, Dr. Michael Barnsley and Professor Stephen Hawking.

Deep Animated Zoom - This 5 minute video gives a sense of the infinite complexity and depth of the Mandelbrot Set. The maker of the video states that a 12 core computer spent 6 months performing the calculations necessary to render all the frames.