It's pretty easy to do plaids and tartans if you paint on fondant, but that can give you muddy colors. The cake in the photo here was done with candy clay strips applied to a flat piece, and food coloring. The downside to doing it like this is that you end up with a raised pattern.
To get the pattern flat, you need to cut pieces out and add them back in in different colors, like marquetry. (If you want to see some amazing marquetry, check out this blog: http://surfacefragments.blogspot.com/2010/07/masterpieces-of-marquetry.html) This isn't nearly as complicated as that, it's more like quilting.
With quilting, you make a patterned block and repeat it over and over, sometimes turning the pattern in different directions. But it's the same pattern. With tartans and plaids, the basic pattern is repeated and you just have to figure out where the repeats happen.
The pattern that the question was about was this photo of bow ties, and I decided to use the bottom pattern because it had the best repeats to demonstrate.
The white bar has a little notched thing going on in the dark part inside it, and I opted to simplify that to make this easier on myself. If you want to recreate a small detail like that it's easy, using the basic method I'm going to show here.
So the repeats in this pattern are the white bar with the dark line inside, and the red section with blue stripes in between. I started with the red part and made a large block of red, then added some gum glue to it and layered blue and red strips to the top to form the stripes. I wrapped that up and let it sit for a few hours to give it time to stick to itself.
I then did the white stripe section with the blue stripe inside by layering those pieces. Same process, use gum glue to attach them and wrap them up to sit for a while.
For this, try to make the strip about the width that the finished stripe will be so that you don't have to press on it to flatten it out too much. That will distort the stripe, and you want to avoid that.
Next, roll out a piece of backing paste to put the patterned pieces on. Get this as thin as you can but not paper thin. If you put it through a pasta roller, I'd do it to about a 4 on the Kitchenaid.
Start cutting thin blocks of the red block off. Try to get them as thin as you can but thick enough that they hold their shape. 1/16- 1/8" is good. To cut the block, I use a blade that's designed for polymer clay. It's basically a long razor blade, and it makes a good clean cut without pulling on the paste and distorting the pattern.
Using gum glue, put these strips on the backing paste in a diagonal pattern. Trim the edges off and use the trimmed pieces to fill in any gaps at the base of the backing paste.
Keep lining up the strips until the whole piece of backing paste is covered. Trim the edges. I wasn't making much effort to keep the stripes even in this example, but if you're doing this for an actual cake you should try to keep the stripes as straight as possible while you're placing them on the backing paste.
Next step...Remove a strip of the pattern so that you can use your marquetry techniques to insert the new color into the pattern. I looked at the places where the strips joined and used the seams as the spot to cut. Then I cut pieces out so that the red would be square-shaped between the white sections.
I used the straight blade again to mark the cuts, then removed the paste with a spatula. Put the spatula blade straight down into the cut, then flip the paste out.
So now you have little ditches where the white strips will go. Cut them off of the block the same way you did the red, then place them in the gaps. be really careful here, you really have to make an effort to keep the stripes straight. You could also do this by cutting individual stripes and inserting them one by one, but they would be hard to handle because of how thin they are.
(As an aside, you COULD do this entire thing by rolling out thin pieces, cutting them and layering them one by one on the backing paste. The downside to that is that the thin stripes would be more likely to stretch than if you do it using the block to start.)
If you need to use some more gum glue in the ditches, do so that the stripes stick well. You can press them down with a rolling pin, but don't roll it because that will stretch the stripes.
Cut a piece off of the end to be the center for the bow.
Trim the piece so that it curves at the center like the tie in the photo.
You should be able to pick the piece up and move it around without the pattern coming off. If it does come off you should stick it down with more gum glue. Wrapping it up and leaving it for a while would be good at this point.
When it's been sitting and sticking to itself for a while, fold the edges over to the center. I turned it over and used the other side for the front of the bow, adding the strip to the center and putting plastic wrap in the bow to hold the loops up to dry.
Trim off any rough edges that might have separated or just didn't adhere correctly.
Check the pattern carefully to press down any pieces that might have separated from the backing strip when the loops were folded over. Let the bow dry...
If you do this with candy clay make sure that the clay itself is soft and pliable. If it hardens up and dries out mid-process it can crack when you try to bend it.
Pay attention to the stripes, which I didn't do since this was for demonstration purposes only...If you need to straighten up the stripes you can usually just rub them slightly with your finger and it will push the color slightly in one direction or the other. When you put the stripes in the ditches they need to fit down inside the ditch completely...See the white stripe to the right of the center? It kind of stuck up out of the ditch, and I was too lazy to trim it down. But it looks too fat in the end, so now you see what will happen if you don't make sure everything fits!!!
That's the basic idea, though, without the precision...Add the precision and you can do some nice plaids that look like one continuous sheet of paste without seams or raised pieces.