The size, and shape of the original sheet of paper will influence this pattern as well as how you fold it up.
I have a tool called a tracing wheel which is used in dressmaking, but I love to draw with it. By going over a simple pencil outline on one face of the folded paper the outlines are transferred to the hidden faces of the paper.
Areas can be blocked out so they are positive or negative shapes, areas could be cut out also.
If you don't have a tracing wheel maybe you could find tracing paper or some light weight paper which will show the original drawn outline, trough to other folded paper surfaces.
This is an example photographed in my studio (no room at home for larger work!) I use the technique to make patterns from leaf shadows
Lastly a link to instructions for making a kaleidoscope.
Researching for this post I came across a suggestion about not only putting beads etc in the end but also using the tube to look at anything - flowers, leaves, clouds. A nice reminder that anything you come across has a few hidden depths or aspects that you haven't thought of before.