In a kaleidoscope, the view you see is of beads being reflected several times over. This means there is one main pattern and it is mirrored 6 more times creating 7 of the pattern. (Or at least this is the usual. The amount of mirrors dictates how many times the image is reflected so it can be more or less depending on the kaleidoscope.) These 7 identical patterns make one kaleidoscope image. Remember that when making a kaleidoscope tile mosaic.
Start by measuring out the area you will be adhering the tiles to (whether it be a table top, wall, etc.). Then decide how many sections you want to divide this space into. A kaleidoscope always has a center image so start there and decide what you have room for around it. If you have a 12 by 12 inch surface to work on, you can have a 4 inch center plus 6 kaleidoscope copies surrounding the center. It’s important to figure out your math because a kaleidoscope has perfect symmetry, which you are trying to replicate without the use of trick mirrors.
Since you will need several exact copies of the center pattern you will need an exact amount of matching tiles. You can use pre-cut tiles, cut the tiles yourself, or you can do this the hard way by breaking up the tiles with a hammer and attempting to match them up in a symmetrical way. Obviously the first two options are the simplest. Since you have already decided how many copies of the pattern you will need to make, pick out your tiles according to those calculations. This means if you pick out some red triangles and you will be making 7 identical patterns you will need to pick out 7 red triangles. If you want more then one red triangle in each pattern, be sure to pick out a multiple of 7, say 21 so each pattern gets 3 red triangles. Buying regular tiles that you will either have cut for you or will cut yourself, is pretty much the same method of math. If you are going to cut each tile into 4 pieces and you have 7 patterns to make, you will need to buy a minimum of 2 tiles. If you wanted to put 5 pieces of this same cut tile into each pattern you would need to buy at least 9 tiles. Ultimately, the math is your pattern (1) times the kaleidoscope effect (7) times the amount of each tile piece per pattern (5). This equation will help make your planning simpler.
When it comes to actually making the kaleidoscope mosaic, you must lay it out first. There is nothing worse then putting down the mortar and discovering your mistakes while fighting drying time. You can lay out your tile mosaic onto the surface you will be tiling. Even better is to cut a piece of paper the exact size and shape of the surface and use that as a template. It may help to draw pencil lines of each section of the kaleidoscope image (so if you chose 7 then you make seven equal sections). Then start in the center and lay out your first pattern. Now go around the center exactly duplicating that first pattern in each of the other sections. If you happen to find there is a slight gap between each section, you can either leave it bare because the grout will fill it in or you can fill it in will small tile pieces, preferably all of the same color so they won’t distract from the symmetrical pattern.
Once you have everything all planned out, mortar the surface and carefully begin placing the tile, being sure not to mess up the pattern. This is where having the tile mosaic on a piece of paper is helpful because you can just take one piece off at a time and make sure you are still keeping the pattern. Pay careful attention to place the tiles onto the surface exactly like they were on the paper. When finished let dry, grout, and admire your work.