Wednesday, October 19, 2011

more ruffly things



The first image (actually they're switched and it's the 2nd) was my first hyperbolic plane. It starts with 1 heptagon in the middle. The second layer puts 7 heptagons around it. The 3rd layer is 22 heptagons around. The 4th layer would have been 56 heptagons, but after I had done some of it I took it out, because, as I said in the earlier post, the piece was sticking out too far from the body for a pendant. It was nicely ruffly however.
I can't quite figure out the math for why the progression is 1,7,22,56. The first 2 numbers are obvious, but then it got wierd. I keep thinking maybe there's a stray octagon or hexagon somewhere, which would screw up the counting, but if there is I haven't found it. Another possibility just occurred to me. Maybe I just counted wrong, and the 3rd number is 21. It gets really hard to keep track of which layer is which, and it seems like they should all be multiples of 7. Oh,well...
The 2nd picture is the ruffle that starts with a tube and gradually flares out till it gets ruffly. This came from reading about all the crocheted coral reef forms. I loved how the engineers were trying to create the ruffles by scotchtaping bits of graph paper around in a spiral, adding 1-1-1-2 (you can change the algorithm by varying the number of 1s between each 2) and it was really cumbersome. Then one of the female engineers realized you could do the same thing with crochet stitches, and it would be far easier, and would represent it better too. I used a ladder stitch instead of crocheting. As I remember, some of the forms are 1112 and some are 112 (these start to ruffle faster and go really crazy really quickly).
Anyway, I like these, and someday I'll get around to doing something with them, but I probably won't make any more, as they take a loooong time.

1 comment:

  1. I think you counted wrong. I looked at this picture http://en.wikipedia.org/wiki/File:Uniform_tiling_73-t0.png and I counted 21 heptagons in the third ring. No matter though, it's still a fun piece. Are those long colorful beads glass or plastic? I love the colors together.

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