Generation of Chaos using Ramanujans Ternary Quadratic Form

Ramanujans Ternary Quadratic Form represents a series of numbers that satisfy a tripartite quadratic relation. In the present work, we examine the sequence of numbers generated by such forms and other related forms obtained by varying the coefficients and exponents to other values. Chaotic characterization using standard techniques such as Lyapunov Exponents, Kolmogorov Entropy, Fractal Dimensions, Phase Portraits and Distance plots is performed. It is seen that the Ramanujans Form as well as the related forms, when expressed as time series exhibit chaotic behavior. Finally, we conclude by stating that the form to series mapping outlined in the present work enables the generation of chaotic signals without the need for excessive system complexity and memory, and we note that such chaotic signals can be used as the basis for carriers in secure communication systems.