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We describe a search for plane-filling curves traversing all edges of a gridonce. The curves are given by Lindenmayer systems with only one non-constantletter. All such curves for small orders on three grids have been found. Forall uniform grids we show how curves traversing all points once can be obtainedfrom the curves found. Curves traversing all edges once are described for thefour uniform grids where they exist.

Plane-filling curves on all uniform grids