|
![](/i/fill.gif) |
>> 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*
Post a reply to this message
|
![](/i/fill.gif) |