Self-avoiding space-filling folding curves in dimension 3
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929673607315456 |
|---|---|
| author | Oger, Francis |
| author_facet | Oger, Francis |
| contents | 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 $R^{3}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06888 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-avoiding space-filling folding curves in dimension 3 Oger, Francis Combinatorics 05B45 (Primary) 52C22, 52C23 (Secondary) 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 $R^{3}$. |
| title | Self-avoiding space-filling folding curves in dimension 3 |
| topic | Combinatorics 05B45 (Primary) 52C22, 52C23 (Secondary) |
| url | https://arxiv.org/abs/2501.06888 |