Incommensurate Numbers, Continued Fractions, and Fractal Immittances

Continued fractions have a rich tradition in the theory of numbers; e.g., non-terminating con-tinued fractions represent irrational numbers. It will be shown that a class of continued fractions possess the property of self-referential decomposition, and their interpretation in the form of non-terminating ladder circuits gives rise to fractal immittances with potential analogies to rough surfaces, thin cermet films, as well as to the internal void network structure of thick films.