Quad Bulge How To

This is how I made my Quad Bulge piece found here: [link] (and V2 here [link] This version I properly inked and shaded)There is a more detailed explanation there, but it's much easier to do with pictures. This is fairly self-explanatory, I think, for anyone who has done knot work before. The picture on the left is a quick tutorial type drawing and the right is the original sketch.

On the left picture it is regular grid paper. The dark blue lines represent the new grid in order for the knot to bulge. You are able to break your lines anywhere as if you were using a normal grid. (Yes, I know some style of design uses dots, which I kind of like better, but I learned this way and it's easier for me to conceptualize.) The yellow lines represent the first incarnation of the knot. As you can see in the middle section, I only drew in one diagonal to show how each line is moving, almost like a wave, instead of the usual straight lines knot work does. Lastly, the purple represents the thickening of the ribbon, which you should know already. The tricky part here is to keep the middle squares roughly the same size. This is the main part of the illusion. If you draw them larger, the ribbon will turn out to be a uniform width. As you go along, make sure as the ribbon widens or shrinks in width, then keep the over-under lines connected.

Also note, the number of units per side. There are 15 across and 19 down. Because I chose to have the half squares vertically, the across is effectively 14, i.e. if you count the number of times the knot itself touches the top, it peaks at the points of the divisions, not the middle of the squares. Because this is 14*19, you know it will be one knot. Anytime you have a rectangular knot, as long as the width and height have no common denominators, it will be a single knot. So even numbers are tricky to do; you can only pair them with a prime number to get a single knot, i.e. 10*11 will be a single ribbon but 10*12 will not. Odd numbers are not out of the question, but even something like 3*9 would not be a single knot. So I try to stick with a prime number and then anything smaller. If P is prime, then any grid P * P-1 will be a single knot. If P= 23 then 23*22 will be a single knot. Hmm, that's not the most efficient formula. If P is prime, W is width, and H is height, then if H equals P and W is less than P, there will be one knot. If anyone cares to correct me or inform me of a condition that is untrue for, please do so. I came up with it on the spot.

The picture on the right is the original sketch done on white paper with non-photo blue pencil. It's odd how you can scan in the color, but it doesn't show up on a photo copy. Which is what I did. I photocopied this page and shrunk it by about half then colored directly on that. I should have inked the copy first, then recopied it for darker lines, but regardless, Quad Bulge turned out well.