Strings-as models of computational strucure, including data and process, substring functions
Vibrating String Signature
If a vibrating string is attached at one end, histone tails for example, then the free end necessarily follows some path, or signature. Consider a paintbrush attached at the free end and tracing out the 3d path traveled.Proteins are a subclass of "strings" where certain specific geometric properties hold. The carbon atoms of the backbone are at specific distances and angles from each other. The backbone consists of three covalent bonds for each peptide in the chain of peptides which make up the protein. Here are examples of such vibrations and the 3 dimensional structures created...
The relative rotation velocities for the 29 spinning covalent bonds which generated the first "face" in the above image is: 0.001,0,0.001,0.001,0,0.001,0,0,0,1,2,0,1,2,0,1,2,0,2,4,0,4,2,0,2,0.001,1,1,1
These strings should not be confused with the usual use of the term "string" in computer science, as in this article on string operations.
These string operations are stored in a chain of covalent bonds connecting a collection of atoms. The rotations of these bonds around succesive atoms is a powerful computational medium.
Strings admit the following interpretation as nodes on a graph:
- Fixed-length strings can be viewed as nodes on a hypercube
- Variable-length strings (of finite length) can be viewed as nodes on the k-ary tree, where k is the number of symbols in Σ
- Infinite strings (otherwise not considered here) can be viewed as infinite paths on the k-ary tree.
The natural topology on the set of fixed-length strings or variable-length strings is the discrete topology, but the natural topology on the set of infinite strings is the limit topology, viewing the set of infinite strings as the inverse limit of the sets of finite strings. This is the construction used for the p-adic numbers and some constructions of the Cantor set, and yields the same topology.