Insertions refinement for shuffle-greedy growth sequences

The tensegrity growth sequences in the previous post show that leaving the order of insertion edits to chance can lead to unnecessary instabilities.

For example, it is not necessary to pass through a stage as unstable as the 2-hole ladder (below) in growing a cube.

2-hole ladder: an unstable stage in previous growth sequence of a cube.

By attempting to alternate polarity in insertions, we get this alternate growth sequence for a cube, which still has 8 stages:

Growth code:/n/.us/.ns/...uss

Growth sequence:

np (3-strut)

nudp (2-prism)

nupd (tetrahedron)

nnpupd (eared tetrahedron)

nnuppd (3-prism)

nnuudppd (camp chair)

nnuupdpd (boat dual)

nnuuppdd (cube)

The same strategy applied to the dodecahedron gives a growth sequence of the same number of stages (29) that successfully alternates insertion polarity all the way through.

/u/1ns/3us/2nss/5uss/3nsss/7uss/5nsss/9uss/7nsss

ud
unpd
undp
undudp
undupd
unnpdupd
unndpupd
unnduppd
unnduudppd
unnduupdpd
unnduuppdd
unnnpduuppdd
unnndpuuppdd
unnndupuppdd
unnnduupppdd
unnnduuudpppdd
unnnduuupdppdd
unnnduuuppdpdd
unnndnpuuuppdpdd
unnndnupuuppdpdd
unnndnuupuppdpdd
unnndnuuupppdpdd
unnndnuuuudpppdpdd
unnndnuuuupdppdpdd
unnndnuuuuppdpdpdd
unnndnunpuuuppdpdpdd
unnndnunupuuppdpdpdd
unnndnunuupuppdpdpdd
unnndnunuuupppdpdpdd

Growth sequences for some simple tensegrity surfaces

Growth Sequence for a Tensegrity Tetrahedron

/u/1ns

Growing a tensegrity tetrahedron, stage 1. ud (3-strut)

Growing a tensegrity tetrahedron, stage 2. unpd (2-prism)

Growing a tensegrity tetrahedron, stage 3. undp (Tetrahedron)

Growth Sequence for a Tensegrity Cube

/n/1n/2uss/3uss

Growing a tensegrity cube, stage 1. np (Three-strut)

Growing a tensegrity cube, stage 2. nnpp (2-prism)

Growing a tensegrity cube, stage 3. nnudpp (2-hole ladder)

Growing a tensegrity cube, stage 4. nnupdp (Eared tetrahedron)

Growing a tensegrity cube, stage 5. nnuppd (3-prism)

Growing a tensegrity cube, stage 6. nnuudppd (Camp chair)

Growing a tensegrity cube, stage 7. nnuupdpd (Boat dual)

Growing a tensegrity cube, stage 8. nnuuppdd (Cube)

                                         Growth Sequence for a Tensegrity Dodecahedron

               /uu/1nss/2nss/3nss/5ns/7n/8usssss/9ussss/10usss

Growing a tensegrity dodecahedron, stage 1. ud (Three-strut)

Growing a tensegrity dodecahedron, stage 2. udud (2-prism)

Growing a tensegrity dodecahedron, stage 3. unpdud (2-hole ladder)

Growing a tensegrity dodecahedron, stage 4. undpud (Class ring)

Growing a tensegrity dodecahedron, stage 5. undupd (3-prism)

Growing a tensegrity dodecahedron, stage 6. unnpdupd (Camp chair)

Growing a tensegrity dodecahedron, stage 7. unndpupd (Boat dual)

Growing a tensegrity dodecahedron, stage 8. unnduppd (Cube)

Growing a tensegrity dodecahedron, stage 9. unnnpduppd (Eared cube)

Growing a tensegrity dodecahedron, stage 10. unnndpuppd

Growing a tensegrity dodecahedron, stage 11. unnndupppd (5-prism)

Growing a tensegrity dodecahedron, stage 12. unnndnpupppd

Growing a tensegrity dodecahedron, stage 13. unnndnuppppd

Growing a tensegrity dodecahedron, stage 14. unnndnunpppppd

Growing a tensegrity dodecahedron, stage 15. unnndnunudpppppd

Growing a tensegrity dodecahedron, stage 16. unnndnunupdppppd

Growing a tensegrity dodecahedron, stage 17. unnndnunuppdpppd

Growing a tensegrity dodecahedron, stage 18. unnndnunupppdppd

Growing a tensegrity dodecahedron, stage 19. unnndnunuppppdpd

Growing a tensegrity dodecahedron, stage 20. unnndnunupppppdd

Growing a tensegrity dodecahedron, stage 21. unnndnunuudpppppdd

Growing a tensegrity dodecahedron, stage 22. unnndnunuupdppppdd

Growing a tensegrity dodecahedron, stage 23. unnndnunuuppdpppdd

Growing a tensegrity dodecahedron, stage 24. unnndnunuupppdppdd

Growing a tensegrity dodecahedron, stage 25. unnndnunuuppppdpdd

Growing a tensegrity dodecahedron, stage 26. unnndnunuuudppppdpdd

Growing a tensegrity dodecahedron, stage 27. unnndnunuuupdpppdpdd

Growing a tensegrity dodecahedron, stage 28. unnndnunuuuppdppdpdd

Growing a tensegrity dodecahedron, stage 29. unnndnunuuupppdpdpdd (Dodecahedron)