### Tag-systems for the Hilbert curve

*Patrice Séébold*

#### Abstract

*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.

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