Formal Grammars Generating Fractal Descriptions of Molecular Structures

Abstract

Simple rewriting rules are used to produce alphanumeric strings that embed fractal number sequences and are directly translatable into descriptions of hydrocarbon structures of considerable complexity, featuring hierarchical schemes. Rotations of the alphanumeric strings lead to radical rearrangements of the corresponding structures, which lose their initial schemes and become much less predictable, featuring different topologies of polygonal cycles. This shows that a complex and not necessarily ordered molecular structure may nevertheless have a relatively low algorithmic complexity. The variety and versatility of reorganization in chemical topology, due to the nonlocal representation of bonds in the coding string, may have played a role in prebiotic chemistry.