Hilbert words correspond to finite approximations of the Hilbert space filling curve. The Hilbert infinite word H is obtained as the limit of these words. It gives a description of the Hilbert (infinite) curve. We give a uniform tag-system to generate automatically H and, by showing that it is almost cube-free, we prove that it cannot be obtained by simply iterating a morphism.

Source : oai:HAL:lirmm-00184092v1

Volume: Vol. 9 no. 2

Published on: January 1, 2007

Submitted on: March 26, 2015

Keywords: Peano curves,Hilbert curve,Hilbert words,tag-systems,D0L-systems,cubes,repetition-free words,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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