Aharon Rabinowitz has a new QuickTip on Creating 3D Kaleidoscopic Effects. There's also some resources on 2D kaleidoscopes below the fold.
CMD has a tutorial (below) on creating 2D kaleidoscopes in After Effects. As many have, instead of the built-in CC Kaleida, they used Pete'sPlugins, which is no longer developed. You could also use Sapphire Kaleido, AIST ProFX Xkaleido, or the unique Omino Kaleidoscope from the free Omino After Effects Suite (demo below). Storek nVeil, a Mac FxPlug, is another possibility; see the review by Oliver Peters.
You can also create kaleidoscopic elements from Shape Layers; see the excerpt Motion Graphics with Adobe Creative Suite 5 Studio Techniques: Designing Backgrounds for some discussion.
Here's something from reanimatr, who used Particular 2 to create something different: