Chaotic computation

Chaotic Computation is the exploitation of chaotic systems to perform computational tasks. The abundance of uncountable distinct behaviours by chaotic systems, along with their embedded determinism, position such systems as perfect candidates for developing a new computational environment. The present dissertation focuses on algorithms developed over the past decade within the realm of Chaotic Computation. After a brief exposition of general Chaos Theory, we proceed to give detailed instructions for performing such algorithms, as well as specific examples of implementations. We begin with multiple methods for number representation and basic arithmetic manipulations, providing from the start evidence of the flexibility of Chaotic Computation. The compatibility with Turing machines is subsequently shown through an algorithm for logic operations whose general form is a recurrent theme. We soon though, proceed further than Turing machines and present a solution to the Deutsch-Jozsa problem, of arbitrary binary functions. Even more, a practical issue is also handled by showing how chaotic systems have a natural way for selecting matches of a searched item from within an unsorted database. Finally we present our latest results in handling “prolonged” evolution of chaotic systems. Specifically we demonstrate the dominance of selecting the appropriate behaviour, for a computational task, over being exact with specific state values, or even confined to specific physical quantities.