Hello. Congratulations on taking on a very interesting yet challenging topic. Fractals are everywhere...most people just don't realize. If you do a simple google search of "fractals practical applications," you will see many different practical applications.
One suggestion and probably the easiest for a science fair topic is to explore fractals in nature. You already alluded to this in your summary of the PBS program (I also saw the program...it was awesome!). But, why DO they exist in nature? On the surface, fractals seem like utter chaos. However, it actually increases the probably of survivability by providing efficient means for such processes as gas exchange and sunlight absorption.
Have you checked out this recommended topic on fractals?http://www.sciencebuddies.org/science-fair-projects/project_ideas/Math_p013.shtml
Take a look. You could expand this project to explore fractals in nature, or whatever other practical application you find through your research. For my recommendation, a simple google search of "fractals in nature" provide several websites that will be a great start to your project.
Best of luck. Please don't hesitate to write back with further questions!