Chaoscope
This wonderful picture is made in the Windows freeware Chaoscope by Ralph Abraham.

Does anyone know if there is something similar for the Mac, or if it is possible to port it to OS X? See more pictures made with Chaoscope here and here.
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You can achieve very similar images in Electric Sheep Screensaver (http://electricsheep.org/), an open source screen saver that downloads new patterns from the online community. Works on many platforms, including Mac.