Stitching Arrowhead Curves: Extending the Sierpinski Arrowhead Curve to Higher Dimensions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910191608397824 |
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| author | Zimmermann, Eric Bruckner, Stefan |
| author_facet | Zimmermann, Eric Bruckner, Stefan |
| contents | The Sierpinski triangle and the Sierpinski arrowhead curve are both defined in dimension 2 and can be used to model the same fractal. While a natural extension of the triangular construction to arbitrary dimensions exists, an analogous extension of the curve representation does not. In this article, we analyze the properties of the two-dimensional Sierpinski arrowhead curve to formulate an extension to arbitrary dimensions based on reproduction rules. Building on this formulation, we demonstrate a way to visualize such curves in a comparative manner across levels. Finally, as geometric patterns have a long history in the arts, and especially in fashion, we exemplify this visualization approach in knitwear, specifically in the yoke of a sweater. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19287 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stitching Arrowhead Curves: Extending the Sierpinski Arrowhead Curve to Higher Dimensions Zimmermann, Eric Bruckner, Stefan Graphics The Sierpinski triangle and the Sierpinski arrowhead curve are both defined in dimension 2 and can be used to model the same fractal. While a natural extension of the triangular construction to arbitrary dimensions exists, an analogous extension of the curve representation does not. In this article, we analyze the properties of the two-dimensional Sierpinski arrowhead curve to formulate an extension to arbitrary dimensions based on reproduction rules. Building on this formulation, we demonstrate a way to visualize such curves in a comparative manner across levels. Finally, as geometric patterns have a long history in the arts, and especially in fashion, we exemplify this visualization approach in knitwear, specifically in the yoke of a sweater. |
| title | Stitching Arrowhead Curves: Extending the Sierpinski Arrowhead Curve to Higher Dimensions |
| topic | Graphics |
| url | https://arxiv.org/abs/2604.19287 |