ABSTRACT
This chapter shows how symbolic dynamics are not just a tool to study other dynamical systems, but are interesting dynamical systems in their own right. The primary focus of topology is to determine when one mathematical object can be continuously deformed into another. The shift of finite type in exploration is sometimes called the golden ratio shift or the Fibonacci shift. The golden ratio is defined to be the ratio that has the additional property. One of the most interesting places that this remarkable constant arises is in the Fibonacci sequence where it can be shown that the ratio of consecutive Fibonacci numbers approaches.
