The central source for quartz composer creations.
A node-based tool from Apple for building real-time motion graphics on Mac OS X. You wire patches together instead of writing code. Compositions are saved as .qtz files.
It shipped as part of Apple's developer tools (Xcode / the Graphics Tools package) on older versions of Mac OS X. It is not included in current toolchains.
Not reliably. Apple deprecated it and stopped shipping it, so opening old compositions usually means keeping an older Mac OS X machine or a virtual machine around.
VDMX and Vuo are the usual choices for live visuals, and TouchDesigner for heavier work. Origami, used for interface prototyping, began as a set of Quartz Composer patches.