Geodesic
On traversing labyrinths by automata in $n$-dimensional space
Diskretnaya Matematika, Tome 12 (2000) no. 4, pp. 121-137.

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The problem of traversing spatial labyrinths by automata is considered. It is proved that there exists an automaton that makes one unremovable mark (colour) on vertices of a labyrinth and traverses an arbitrary $n$-dimensional rectangular labyrinth. 
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A. Z. Nasyrov. On traversing labyrinths by automata in $n$-dimensional space. Diskretnaya Matematika, Tome 12 (2000) no. 4, pp. 121-137. http://geodesic.mathdoc.fr/item/DM_2000_12_4_a9/

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