Aharon Rabinowitz has a new QuickTip on Creating 3D Kaleidoscopic Effects:
Of course most people are familiar with 2D kaleidoscopes in AE, and although there's noise, there's not depth of coverage for this type of effect.
CMD has a tutorial (below) on creating 2D kaleidoscopes in After Effects. As many have, instead of the built-in CC Kaleida, they used PetesPlugins, 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).
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: