A gasket construction of the Koch snowflake and variations
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866929695048597504 |
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| author | Sargent, Robert C. |
| author_facet | Sargent, Robert C. |
| contents | We introduce a construction of the Koch snowflake that is not inherently six-way symmetrical, based on iteratively placing similar rhombi. This construction naturally splits the snowflake into four identical self-similar curves, in contrast to the typical decomposition into three Koch curves. Varying the shape of the rhombi creates a continuous family of new fractal curves with rectangular symmetry. We compute the Hausdorff dimension of the generalized curve and show that it attains a maximum at the original Koch snowflake. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00815 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A gasket construction of the Koch snowflake and variations Sargent, Robert C. Metric Geometry Functional Analysis 28A80, 28A78 We introduce a construction of the Koch snowflake that is not inherently six-way symmetrical, based on iteratively placing similar rhombi. This construction naturally splits the snowflake into four identical self-similar curves, in contrast to the typical decomposition into three Koch curves. Varying the shape of the rhombi creates a continuous family of new fractal curves with rectangular symmetry. We compute the Hausdorff dimension of the generalized curve and show that it attains a maximum at the original Koch snowflake. |
| title | A gasket construction of the Koch snowflake and variations |
| topic | Metric Geometry Functional Analysis 28A80, 28A78 |
| url | https://arxiv.org/abs/2502.00815 |