Self-avoiding space-filling folding curves in dimension 3

Francis Oger

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arXiv · 2501.06888

Self-avoiding space-filling folding curves in dimension 3

Francis Oger

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Abstract

Various examples of folding curves in $R^{2}$ have been considered: dragons and other square curves, terdragons and other triangular curves, Peano-Gosper curves based on hexagons. They are self-avoiding. They form coverings of $R^{2}$, by one curve or by a small number of curves, which satisfy the local isomorphism property. They were used to define some fractals. We construct an example with similar properties in $R^{3}$.

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Francis Oger. 2025-01-12. Self-avoiding space-filling folding curves in dimension 3. https://arxiv.org/abs/2501.06888

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