Fractals from genomes: exact solutions of a biology-inspired problem

TL;DR

This paper reviews recent work on DNA sequence visualization, revealing self-similar fractal structures in genomes and providing exact solutions for their dimensions using combinatorics and formal language theory.

Contribution

It introduces a novel visualization scheme for DNA sequences and offers exact analytical solutions for the fractal dimensions of genome-derived structures.

Findings

Identification of self-similar fractals in bacterial genomes

Exact calculation of fractal dimensions

Unified approach using combinatorics and formal language theory

Abstract

This is a review of a set of recent papers with some new data added. After a brief biological introduction a visualization scheme of the string composition of long DNA sequences, in particular, of bacterial complete genomes, will be described. This scheme leads to a class of self-similar and self-overlapping fractals in the limit of infinitely long constotuent strings. The calculation of their exact dimensions and the counting of true and redundant avoided strings at different string lengths turn out to be one and the same problem. We give exact solution of the problem using two independent methods: the Goulden-Jackson cluster method in combinatorics and the method of formal language theory.