The coordinate functions of the Heighway dragon curve

D.A. Caprio

Chaos, Solitons & Fractals, 2025, vol. 201, issue P2

Abstract: In this work, we investigate the coordinate functions of a generalized Heighway dragon curve and analyze the fractal structure of their graphs using box-counting dimension. In particular, we study the coordinate functions xθ and yθ of the dragon curve for angles π3<θ<5π3, and establish that the box-counting dimension of their graphs is 1−log(cosα)log2, where α=(π−θ)/2.

Keywords: Heighway dragon; Paper-folding; Box-counting dimension; Coordinate functions (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:201:y:2025:i:p2:s0960077925013141

DOI: 10.1016/j.chaos.2025.117301

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