The Mandelbrot set 1

CD4a, the Mandelbrot set fractal in black and white.

Here is a fine art print of this picture.

The Mandelbrot set is connected (see Sutherland's book, or these notes, for the definition of a connected set).

The colouring method used to create this picture calculates the (minimum) distance from a point (pixel) to the boundary of the Mandelbrot set. This distance is then used to assign a grey-scale colour to the pixel. This is the same colouring method as the one used for the picture CD4b. The only difference between these two pictures is in the colour palette used. (See this article for other methods of colouring the Mandelbrot set and Julia sets.)