The Mandelbrot set has fascinated mathematicians and scientists - and other kinds of people, too - for some decades now, especially since the advent of powerful computers made producing its image very simple. Magnifying any interesting-looking area will simply produce more fascinating detail, and there's no end to it - in theory. In practice, it's limited by the ability of the computer to deal with many decimal places. The image above is a portion of the image below, much magnified (and colour added.)
When I first tried to make the Mandelbrot set image, 23 years ago, my PC had to be left on all night in order to give it time to draw it. I programmed it in the language called "C." Now, my very ordinary laptop takes just a few seconds to produce a colour image. Here is an image of the complete set: Those filaments wandering out from the main mass can be magnified to show the kind of detail in the first picture.
