Why I Like Maths - A Visual Explanation - Enter the Mandelbrot

Source: http://commons.wikimedia.org/It’s about patterns, logic, beauty and infinity.  The way I can demonstrate is visually with fractals and specifically The Mandelbrot Set discovered as recently as 1980. 
The Mandlebrot set is a pattern that’s self replicating and unique, its simple and its complex  and its beautiful. It seemingly goes on forever.
Source: http://commons.wikimedia.orgIt’s been called the definition of infinity and the “thumbprint of God”. I’m inclined to think the latter is true as you don’t have to look very far in the physical world to find Mandlebrot designs – carved in stone on Indian temples, under the microscope, in the fronds of the weedy sea dragon – the list is as endless as a fractal.
I’m not very good at mathematical writing but the best way to explain it that I’ve found is an article by Dave Dewey Introduction to the Mandelbrot Set - A guide for people with little math experience.
Source: http://commons.wikimedia.org identical to the whole. In fact, the Mandelbrot set is infinitely complex. Yet the process of generating it is based on an extremely simple equation involving complex numbers. “
Fractals are a lot of fun for kids and there are a number of free on-line generators such as Easy Fractal Generator and  Fractal Poster.
Another good place to go is You Tube where in a series of 6 videos science fiction author Arthur C Clarke introduces the Mandelbrot set

Arthur C Clarke – The Colours of Infinity 1 of 6Arthur C Clarke – The Colours of Infinity 2 of 6Arthur C Clarke – The Colours of Infinity3 of 6Arthur C Clarke – The Colours of Infinity 4 of 6Arthur C Clarke – The Colours of Infinity 5 of 6
Arthur C Clarke – The Colours of Infinity 6 of 6