Abstract
Iterated function systems can be used to produce a representation of complex images. It has been recently shown that visual representation of the structure of long (2-100 K) sequences by reversing the iterated function system (IFS) technique can be produced, 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. Non-uniformity of the distribution of subsequences produces non-uniformity in the CGR. The CGR is a picture of the sequence, often with visually striking features corresponding to sets of subsequences. This chapter 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 useful for exploring features of CGRs. Finally, several extensions to the basic CGR algorithm are proposed.
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