This is a specific type of fractal, (some would argue that it is not really a fractal at all, but they are included as a type in Fractint, so I include them here. Here's what the Help file has to say about lsystem images:
"Using a turtle-graphics control language and starting with an initial axiom string, carries out string substitutions the specified number of times (the order), and plots the result.
What that all boils down to is that you give it a specific set of rules, then tell it how many times to apply the rule. In this gallery, this is pretty easy to see. If you look at the file name, you will see that it ends with a number. This is the number of iterations specified. Take a look at the difference between executing a rule 2, 4, or 8 times. It's kind of cool.