A Kaleidoscope is an optical instrument with two or more reflecting surfaces inclined to each other in an angle, so that one or more (parts of) objects on one end of the mirrors are seen as a regular symmetrical pattern when viewed from the other end, due to repeated reflection…
How to create it in Blender?
One possible solution is to model the instrument inside of Blender, and consider it as a some sort of simulation… actually some one did it ! This solution is time consuming, and may take a long time to render.
My solution is to fake the reflections using the UV Map, so, if you fold the UV island in a particular way, you will get a very similar results.
Then use a Movie clip or an image sequence as a texture. Choose a nice colorful spot, and that’s it!
You can use the Array modifier to duplicate the Plane.
The cool thing about this technique is, you could preview the animation in real time (in the 3D View), and render it using the Open GL renderer (which is very fast).
Here is the video tutorial.
If you have any questions, let me know in the comments.