Golden Section and Evolving Systems

We present a body of results that demonstrate that the golden section can be implemented in the design of evolving systems. Albeit we only develop the mathematics, both mathematician and computer expert should find the concept clear. Perhaps of particular interest to the number theorist is the observation that the sequence defined by known as the Teleois number system, crops up in our results. Having shown in previous works how this sequence is closely related to the golden section, this manuscript gives further confirmation and the fact that Teleois numbers penetrate the golden section renders it a proportion of great splendour. Our results can find a wide range of applications from information technology to manufacturing.