First, we need to understand what a fractal is. Then we can see how that applies to a story generating system, for this I'll use Microscope as an example since I'm familiar with that game already. Wikipedia:
A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale. If the replication is exactly the same at every scale, it is called a self-similar pattern. An example of this is the Menger Sponge. Fractals can also be nearly the same at different levels. This latter pattern is illustrated in the magnifications of the Mandelbrot set. Fractals also includes the idea of a detailed pattern that repeats itself.
So a fractal is a repeating pattern that displays itself at every scale. Wikipedia has some great pictures of what these look like both computer generated and ones found in nature.
A fractal story generation system then is one that uses the same design patterns at each scale of the story. In a system like microscope, it uses index cards to describe an event. Microscope has 3 main elements
- Period (and over arching happening that denotes a collection of events, usually specifies a time period in the history you are describing)
- Event (a more granular happening that denotes a collection of scenes, usually represents a single major event during the period in which it resides)
- Scene (the most granular happening that can either be role played or described, typically represents a turning point or otherwise pivotal moment during an event)
All of these use the same pattern (except scene, where you have the option to have more description/roleplaying, but it's still very similar). They are simply a description written on an index card.
Additionally, you can break a fractal up into it's smallest piece and still see the pattern of the fractal replicate. Because Microscope is defining a history, you can make the spacing between periods, events and scenes as narrow as you want in your storyline and keep breaking them up, you can also add as many as you want and the game can go on forever.
The contrast here is between a fractal story generator, and say, a linear story generator which would seek to tell events as they happen without using the same patterns over and over (in Microscope the patter is period->event->scene).