>> Has anyone ever used a Julia fractal for anything other than these 
>> trippy videos?
> 
> I would guess there's at least one mathematical result of importance 
> about them, or we'd not be hearing about them so much.

Result #1: Simple dynamical systems can give rise to unpredictable 
behaviour. (The system has to be non-linear though, even if only 
slightly. A perfectly linear system does nothing interesting.)

Result #2: Every basin of attraction contains at least one critical 
point of the map. (Only guaranteed for rational maps though.)

Result #3: The Julia set is the boundary of all basins of attraction 
simultaneously. (Even if there are three attractors, every point of the 
Julia set touches all three basins simultaneously - despite this being 
obviously impossible.)

I could go on...

I have no idea whether these results have any particular *practical* 
usage. But Julia sets do occasionally pop up when people aren't trying 
to do anything related to computer graphics. (Ferromagnatic phase 
renormalisation transforms, anyone?)

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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