As before, on the side with the extra strand, the lower strand jumps over the other strand on that side and the strand on the side after that. As before, I did this counter-clockwise, but clockwise works well, too, as long as you commit and/or figure out how to change directions.
The above is a crude diagram, showing how the traveling thread jumps and where its new position is. After it's in its new position, rotate the disk and continue doing the same thing.
And here is what it looks like so far.
I used 1 blue and 4 green threads this time. It's a cute braid.
If the 9-strand braid was a 4X + 1 and the traveling thread jumps 2X threads, where X=2, then this is 4X + 1, where X=1. It probably generalizes pretty well in theory, but in practice, I don't know how large X can be before the resulting braid is too thick and/or doesn't look right. I also don't know if this works for numbers other that "4" -- what does it look like with 3X+1 or 5X+1, for example. (3X+1=7 when X=2, hmmm)
Another way to think about this braid and the 9-strand one, and also the 7-strand one, is that the number of threads that get jumped over isn't a common denominator of the total number of strands. So, for the 7 strand braid, you get a group of 2 and a group of 5. For the 9-strand braid, it's a group of 4 and a group of 5. For the 5 strand braid, it's a group of 2 and a group of 3. Maybe -- I'm still thinking about this idea. I mean, it does seem kind of obvious that each thread needs to travel along a path that eventually brings it back to where it began while weaving over and under the other threads in some patterned way. So as long as there's a repeatable path, things like denominators and multiples aren't that important, even with disk braiding. But maybe it'll be useful for these simple repeat-one-easy-move kinds of braids.
The Braid Society has a write-up of a few other groupings that work -- two different 10-strand braids (with 11 slots in the disk), either jumping 2 or jumping 3; a 14 strand (15 slots) that jumps 3; and a 20 strand (21 slots) that jumps 7. Those are all fill-the-gap braids as opposed to whatever one wants to call the X+1 braid I'm doing. (These can all be found through the links at https://thebraidsociety.wildapricot.org/Fill-the-gap)
Probably all of this has been worked out by braid mathematicians and/or engineers of factory braiding equipment. But it's kind of fun to think it through. I need to see what, if anything, Noemi Speiser had to say about it. If I can generalize a track plan I can see what other braiding methods end up with the same structure. Plus it kind of reminds me of all those old Spirograph things that are (and were) sold as toys.
Another thing about this braid (and probably others in this family) -- when I first pulled on it, it seemed somewhat elastic and stretchy. But when I tugged on it a bit harder, that seemed to fix the strands in place. Dunno if that's something to do with the acrylic I'm using, or the tension when I braid, the braid structure, etc.
I do like how simple these braids are to set up and braid. And so far, they are attractive braids that hold together and all those other things we expect from a braid.
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