Wednesday, October 6, 2010

Viable Adjacent Letter Mutations

There are some two-adjacent-letter edits (substitutions, insertions, and deletions) that can always be made in an undip word and the result will be another undip word. These special edits, viable adjacent letter mutations, or val mutations, intrinsically satisfy the undip grammar rules, the larger context of the two original adjacent letters need not be consulted. The term "viable," borrowed from biology, here means that the character string that results from a val mutation will indeed be a word in the undip language (and it will therefore weave unambiguously to a specific basket shape phenotype.)

In the tables below, all of the val mutations are summarized in truth table format. The first of the original adjacent letters labels the row, the second the column. The letters that will replace the two original letters are entries in the table, with e symbolizing deletion of both letters, and a blank entry indicating that no val mutation of that type (substitution, insertion, or deletion) can be made for those two letters.

Some other two-adjacent-letter edits may be viable in certain special contexts, for example insertion of the reversed spikes du and pn , but in the worst case, full context information would be needed to determine if the insertions are viable. In this sense, what are termed here val mutations are context-free.

Gene-Splicing Baskets

Starting with undp, an undip word for tetrahedrane, 

concatenate ud, an undip word for acetylene... 

...and get undpud, or benzvalene.

Insertion of undip words works just as well as concatenation. At any place in an undip word, insert another undip word and the result is a new undip word describing a hybrid shape. The new shape is 2-edge connected where the two original shapes are tenuously joined.

The structural weakness of this 2-edge join can later be healed by viable adjacent-letter (val) mutations. Val mutations are substitutions, insertions, or deletions of two adjacent letters that can be made without reference to context because they intrinsically satisfy the undip grammar rules.