## I need a 2-dimensional pattern for using 3 colors

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(I also need a better title for this post.)

After two years of knitting, which included about 8 months of not knitting and then 3 months of knitting every spare second in order to finish, I’ve almost completed 49 squares for an afghan.  Now I just have to put it all together.

So here’s what I have:
24 squares in single colors (8 each of Blue, Green, and Yellow)
25 squares in multi colors (roughly 8 of each pair of colors, although some use all three colors)

I want to put them into a 7×7 grid in a way that alternates single and multi-colored squares, and while I can do this according to trial and error I feel like there should be a better way.  The end result would look something like thing:

(This is the last time I made an afghan, which also took me 2 years to do.  Apparently I like this triple of colors, though I’m using a darker blue and a lighter green this time.)

There ought to be a pattern of how to lay out the squares, probably alternating single and multi-colors, so that the colors are more or less evenly spread over the entire blanket.  There ought to be LOTS of patterns, I think — and probably patterns that generalize to using n×n squares of k colors [or even n×m squares].   Does anyone see anything, obvious or not?  Ideas for where to look would be most welcome!

I’m aware of the irony that my reason for wanting a patterns is to save time for the initial setup, even if I end up switching some stuff around, but I’m spending even more time than I’d save trying to look for a pattern.  Still, in 2+ years if I face this same question again I’m sure all that work will pay off!

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### 6 Responses to “I need a 2-dimensional pattern for using 3 colors”

1. JT Says:

I start in the middle, add an opposite to the four sides, fill in the corners to make a 3 by 3. Then add three to each top, side, and bottom making sure to alternate, and so on. Sometimes I have to switch with something internal because I’m left with something too close to its neighbor, but in general it works for me.

2. Michelle Says:

Have you done a sudoko (number/logic puzzle?) before? At a quilt retreat we used them to arrange fabric for a quilt using the numbers in the sudoko. I too am challenged by coming up with a “random” pattern – I’m much too linear for that but the sudoko puzzles have helped enormously! Granted they are 9×9 rather than 7×7, but you might be able to modify it a bit to help!

3. Ξ Says:

JT and Michelle — thanks! It’s funny, I thought I’d thought about this a lot, but I kept envisioning starting in a corner and it never occurred to me to think about the center.

The sudoku piece would work well I think — after reading your suggestion I first thought that 6×6 might work better than 9×9 (and then I’d just add a row/column) but then I realized that if I break this down into solid and mixed colors, I really have an independent 3×3 and 4×4, and I could use sudoku ideas for both of those and then just blend them.

I’m still searching for a formula (just for fun) but I appreciate these new ways to think about the practical pieces, esp. since I’m only a few days away from the piecing. 🙂

4. colintgraham Says:

It may not be very helpful, but you might like to play with the interactive tartan designer… Tartans are built up from basic patterns and limited ranges of colours, so it may give you an idea or two!

http://www.houseoftartan.co.uk/interactive/designer/index.htm

5. colintgraham Says:

On reflection, I wonder if you could relate this to the famous eight-queens on a chessboard problem, where the queen represents a colour that you don’t want to repeat in the same row or column…

In generalizations from 1×1 to NxN, 2×2 and 3×3 don’t have any solutions, so maybe your problem is in choosing 3 colours! 7×7 has six unique solutions: http://www.durangobill.com/N_Queens.html is as good a starting point as any! 😉

6. Ξ Says:

Thank you colintgraham!

(I also realized after posting above that 7×7 isn’t 3×3 plus 4×4 as I implied — I hate it when my thoughts get ahead of my brain. But it could still be modified I think.)