Folding the Heighway dragon curve
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917365718974464 |
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| author | Chang, Ting-Wu Chen, Liang-Ting Mu, Shin-Cheng |
| author_facet | Chang, Ting-Wu Chen, Liang-Ting Mu, Shin-Cheng |
| contents | The Heighway dragon curve is one of the most known fractal curves. There are two ways to construct the curve: repeatedly make a copy of the current curve, rotate it by 90 degrees, and connect them; or repeatedly replace each straight segment in the curve by two segments with a right angle. A natural question is how do we prove the equivalence of the two approaches?
We generalise the construction of the curve to allow rotations to both sides. It then turns out that the two approaches are respectively a foldr and a foldl, and the key property for proving their equivalence, using the second duality theorem, is the distributivity of an "interleave" operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27302 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Folding the Heighway dragon curve Chang, Ting-Wu Chen, Liang-Ting Mu, Shin-Cheng Programming Languages 68N18 (Primary) 68R01, 00A08 (Secondary) F.3.1; D.2.4 The Heighway dragon curve is one of the most known fractal curves. There are two ways to construct the curve: repeatedly make a copy of the current curve, rotate it by 90 degrees, and connect them; or repeatedly replace each straight segment in the curve by two segments with a right angle. A natural question is how do we prove the equivalence of the two approaches? We generalise the construction of the curve to allow rotations to both sides. It then turns out that the two approaches are respectively a foldr and a foldl, and the key property for proving their equivalence, using the second duality theorem, is the distributivity of an "interleave" operator. |
| title | Folding the Heighway dragon curve |
| topic | Programming Languages 68N18 (Primary) 68R01, 00A08 (Secondary) F.3.1; D.2.4 |
| url | https://arxiv.org/abs/2603.27302 |