Incommensurate Numbers, Continued Fractions, and Fractal Immittances
Abstract
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.
- Publication:
-
Zeitschrift Naturforschung Teil A
- Pub Date:
- November 1988
- DOI:
- 10.1515/zna-1988-1106
- Bibcode:
- 1988ZNatA..43..943L