This monograph originates from a study of the continued fraction [1, 2, 3, ...], which we call the Zopf number. Its origins date back to 1929 when Siegel introduced it as a ratio of Bessel functions. Continued fractions is most often styled classically, and much of the content is formulated through Diophantine analysis. However, in this book aspects of the theory of computation can be used interchangeably through matrices and transducers.We give an introduction to the computational...