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arXiv · 1710.08480

The generalized Sierpi\'{n}ski Arrowhead Curve

András Kaszanyitzky
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Abstract

We define special Hamiltonian-paths and special permutations of the up-facing dark tiles on a checked triangular grid related to the generalized Sierpi\'{n}ski Gasket. Our definitions and observations make possible the generalization of the Sierpi\'{n}ski Arrowhead Curve for all orders. We produce these symmetric recursive curves in many ways by two kinds of asymmetric paths which are in a bijective relation and unambiguously transformable into each other in any order. These node-rewriting and edge-rewriting recursive curves keep their self-avoiding and simple properties after the transformation and their cardinality specifies a new integer sequence. We show a transformation table to change the curves into each other and we give another table to change them into Lindenmayer-system strings both by the absolute direction codes of their edges.

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András Kaszanyitzky. 2017-10-23. The generalized Sierpi\'{n}ski Arrowhead Curve. https://arxiv.org/abs/1710.08480

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