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An interesting class of automatic sequences emerges from iteratedpaperfolding. The sequences generate curves in the plane with an almostperiodic structure. We generalize the results obtained by Davis and Knuth onthe self-avoiding and planefilling properties of these curves, giving simplegeometric criteria for a complete classification. Finally, we show how theautomatic structure of the sequences leads to self-similarity of the curves,which turns the planefilling curves in a scaling limit into fractal tiles. Forsome of these tiles we give a particularly simple formula for the Hausdorffdimension of their boundary.

Paperfolding morphisms, planefilling curves, and fractal tiles