Abstract
While highly recursive infinite treesT do generally contain no recursive infinite path, they do so if sufficiently many cross connections between nodes ofT are recursively given. Applying this technique to 1-dimensional cell spaces, recursive configurations (given by a finite description) which are not Garden-of-Eden, always possess a recursive predecessor. This is in contrast to a known result on 2-dimensional spaces.
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Carstens, H.G., Golze, U. Recursive paths in cross-connected trees and an application to cell spaces. Math. Systems Theory 15, 29–37 (1981). https://doi.org/10.1007/BF01786971
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DOI: https://doi.org/10.1007/BF01786971