A gasket construction of the Koch snowflake and variations
Metric Geometry
2025-02-04 v1 Functional Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2502.00815,
title = {A gasket construction of the Koch snowflake and variations},
author = {Robert C. Sargent},
journal= {arXiv preprint arXiv:2502.00815},
year = {2025}
}
Comments
15 pages, 14 figures