Chaos game visualization of sequences

Abstract

Iterated function systems can be used to produce a representation of complex images. It was recently shown that one can produce visual representation of the structure of long (2–100 K) sequences by reversing the IFS technique, using a fixed set of affine maps and having map selection controlled by the sequence. The resulting Chaos Game Representation ( CGR) is a 1-1 map between plotted points and subsequences. Nonuniformity of distribution of subsequences produces nonuniformity in the CGR. The CGR is a picture of the sequence, often with visually striking features corresponding to sets of subsequences, thus a new set of questions and areas of investigation. This paper presents the technique, several examples using DNA sequences as examples of nonrandom sequences whose structure is of great independent interest, algorithms for approximating arbitrarily closely subsequences corresponding to observable features of the CGR, and a description of a program based on these algorithms that has useful for exploring features of CGRs. Finally, several extensions to the basic CGR algorithm are proposed.