Deformations: 21 genetic variants of udud

This is a recently completed sculpture, Deformations, that I hope to show this July at Bridges 2012 at Towson University in Baltimore, Maryland. It contains the 21 different versions of the digonal prism that can be made from flexeez by playing the individual flexeez either long or short.

Multiple undip words describe the digonal prism. Here are all eight synonyms for the digonal prism in u-n-d-p alphabetical order:

uudd
unpd
udud
udnp
nudp
nnpp
npud
npnp

They all make the same shape, but if you use a consistent coloring convention (I use pink/purple/green, pink = 1st energy color, green = photon color) some will come out colored differently. I tend to remember udud as the undip word for the digonal prism (rather than any of the seven other equally good synonyms,) so that is how I wove these colorings. The choice of word and coloring is really arbitrary, but it helps to be consistent.

Playing the individual flexeez either "long" or "short" produces what a chemist would call a deformation isomer, a chemical structure that differs only in bond length. Each open letter represents a Y-join where two flexeez are added to the work, each closed letter represents a Y-join where one flexeez is added to the work. To annotate the deformation isomers, I markup the undip word, adding two accents to open letters, and one accent to closed letters. Keeping that rule completely consistent, the extra accent that is needed at the first letter (which is always open) is added to the last letter (which is always closed, and where no other accent is ever needed.) I begin weaving by reading the accent at the very end of the word.

Overall, there are exactly one-and-a-half accents (and flexeez) per letter and, of course, there are an even number of letters, 2n, in the undip word. If the shape we are making is unsymmetrical, then all of the different ways of playing the flexeez long or short make geometrically different shapes. Therefore, there will be 2^(3n) different deformation isomers of an unsymmetrical shape. If the shape has some topological symmetry (as the digonal prism does) some of the different markups will describe the same shape. For example, the digonal prism has only 21 deformation isomers, though it has 2^(3*2) = 64 different markups.

Using a prime to indicate a flexeez played long, and a star to indicate a flexeez played short, and always considering the flexeez added at each Y-join in right-to-left, counter-clockwise order (a convention that comes naturally in twog weaving, but is rather arbitrary in weaving flexeez,) here are the 21 markups I wove for Deformations:

1. u''d'u''d'

2. u*'d'u''d'

3. u**d'u''d'

4. u**d*u''d'

5. u**d'u*'d'

6. u''d*u''d'

7. u'*d*u''d'

8. u*'d'u*'d'

9. u*'d'u'*d'

10. u''d*u''d*

11. u'*d*u'*d'

12. u'*d*u*'d'

13. u*'d*u''d*

14. u**d*u**d*

15. u'*d*u**d*

16. u''d*u**d*

17. u**d'u**d*

18. u*'d'u**d*

19. u'*d*u'*d*

20. u'*d*u*'d*

21. u**d'u**d'