Generation of Digital Planes Using Generalized Continued-Fractions Algorithms.

We investigate a construction scheme for digital planes that is guided by generalized continued fractions algorithms. This process generalizes the recursive construction of digital lines to dimension three. Given a pair of numbers, Euclid's algorithm provides a natural definition of continued fractions. In dimension three and above, there is no such canonical definition. We propose a pair of hybrid continued fractions algorithms and show geometrical properties of the digital planes constructed from them.