A new three dimensional approach to the chaos game representation of protein sequences is explored in this thesis. The basics of DNA, the synthesis of proteins from DNA, protein structure and functionality and sequence alignment techniques are presented. The mathematical background needed for understanding the chaos game representation and fractal analysis are briefly discussed. An account of the existing literature on the chaos game representation of DNA sequences and a detailed account of the chaos game representation of protein sequences in two dimensions with its advantages and limitations are presented. We explore a new three dimensional approach to the chaos game representation of protein sequences (3D-CGR) and study its ability a) to determine protein sequence similarity and differences, b) to study the effect of dinucleotide biases at amino acid level on the 3D-CGR derived protein homology, and c) to identify sequence similarity based on shuffled motifs that could be used for studying protein evolution due to exon shuffling.