Well, you can create similar animations or even plain static images for your desktop background using a free software called Apophysis. [Thanks Raj Dash]
The Apophysis software comes preloaded with a big list of fractal flames. You can change their shapes by moving the triangle and circles inside the Transform editor. You can save the fractal animation movie as a series of sequence images on your hard disk.
Raj Dash refers to his gallery of fractal pictures as e-Paintings where I came to know about Apophysis - "The idea is that a tiny bit of input into the system causes great (chaotic) changes." [the origin of universe and big bang theory]
Ultimately, generating fractals is all about writing simple scripts inside notepad and executing them with Apophysis. The language uses the Pascal syntax. Rajahh has another wonderful collection of Fractal Wallpapers.