FRACTAL CANTOR PATTERNS IN THE SEQUENCE STRUCTURE OF DNA

Abstract

The coding parts of DNA sequences are regarded as clusters of connected sites of a random Cantor-like set, while the non-coding parts are regarded as the empty regions of the same set. Under this representation, we find that higher eucaryotes are mapped on random Cantor sets with fractal dimension around 0.85, while lower organisms are mapped on Cantor sets with fractal dimension 1. This result indicates that the coding/non-coding partition in the DNA sequences of lower organisms is homogeneous-like, while in the higher eucaryotes the partition is fractal. This result agrees with the power law distribution observed in the non-coding parts of higher eucaryotes.